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  • Articles  (58)
  • Optimal control  (31)
  • simulation  (27)
  • 1985-1989  (58)
  • Mathematics  (52)
  • Energy, Environment Protection, Nuclear Power Engineering  (6)
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  • Articles  (58)
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  • 1
    Electronic Resource
    Electronic Resource
    On a stochastic description of the time-space behaviour of extratropical cyclonic precipitation fields (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 37-52 
    Details
    ISSN: 1436-3259
    Keywords: Cyclonic precipitation ; mathematical modeling ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A stochastic description is developed for extratropical cyclonic precipitation fields at synoptic and meso scales as they are typically observed by radars over the Earth. This description attempts to account I) for the synoptic scale behavior of a cyclonic storm (its birth, its synoptic scale motion trajectory, and its dissipation) II) for the synoptic-scale organizational structure of subsynoptic precipitation areas (rainbands, precipitation cores and raincells) within a cyclonic storm; and III) for the behavior of subsynoptic precipitation areas, in terms of their births, their spatial configuration evolutions, their motions, and their deaths (dissipation). The precipitation cores and the raincells are taken as the building blocks of the subsynoptic precipitation, areas within a cyclonic rainfield.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543908
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  • 2
    Electronic Resource
    Electronic Resource
    Stochastic analysis of estuarine hydraulics (1989)
    Springer
    Stochastic environmental research and risk assessment 3 (1989), S. 71-84 
    Details
    ISSN: 1436-3259
    Keywords: Hydraulics ; quasilinearization ; simulation ; stochastic ; estuarine system ; Monte Carlo methods ; random differential equations ; parameter uncertainty
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A new methodology is presented for the solution of the stochastic hydraulic equations characterizing steady, one-dimensional estuarine flow. The methodology is predicated on quasi-linearization, perturbation methods, and the finite difference approximation of the stochastic differential operators. Assuming Manning's roughness coefficient is the principal source of uncertainty in the model, stochastic equations are presented for the water depths and flow rates in the estuarine system. Moment equations are developed for the mean and variance of the water depths. The moment equations are compared with the results of Monte Carlo simulation experiments. The results confirm that for any spatial location in the estuary that (1) as the uncertainty in the channel roughness increases, the uncertainty in mean depth increases, and (2) the predicted mean depth will decrease with increasing uncertainty in Manning'sn. The quasi-analytical approach requires significantly less computer time than Monte Carlo simulations and provides explicit
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01544073
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  • 3
    Electronic Resource
    Electronic Resource
    Simulation of the time-space evolution of an extratropical cyclonic precipitation field over USA (1988)
    Springer
    Stochastic environmental research and risk assessment 2 (1988), S. 281-294 
    Details
    ISSN: 1436-3259
    Keywords: precipitation field ; stochastic time-space evolution ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The time-space evolution of an extratropical cyclonic precipitation field over U S A is simulated in a stochastic setting as outlined in Kavvas et al. (1988). The birth of a cyclonic storm is characterized by the simultaneous birth of a cyclone center and births of subsynoptic precipitation areas (SPA) at preferred locations around the cyclone center. The precipitation cores and cells which are used as the fundamental building blocks of the SPAs are approximated by circular precipitation areas (CPA) of different sizes. The time space evolution of the precipitation field after the birth is governed by (1) the movement of the synoptic cyclone described by the cyclone center trajectory, (2) independent nonidentically distributed random velocities of the individual CPAs relative to the cyclone center, (3) the births of new CPAs in time and space relative to the cyclone center, (4) the independent evolution in time of the individual spatially uniform intensities of the existing CPAs, (5) the expansion and shrinkage of the existing CPAs in the course of movement and (6) the dissipation (death) of a random number of existing CPAs within the cyclonic system. The computer simulation, the results of which are presented in this paper, successfully reproduced the general mesoscale and synoptic scale features of the radar detected cyclonic rain fields as observed by Austin and Houze (1972), Houze et al. (1976), Hobbs (1978), Hobbs and Locatelli (1978), Houze (1981), Houze and Hobbs (1982) and others.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01544041
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  • 4
    Electronic Resource
    Electronic Resource
    Uses and abuses of statistical simulation (1988)
    Springer
    Mathematical programming 42 (1988), S. 53-68 
    Details
    ISSN: 1436-4646
    Keywords: Design of experiments ; normal random variates ; pseudorandom ; simulation ; statistical inference
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract More and more problems are being tackled by simulation as large computing costs per hour approach those of mathematicians' time. Abuses of simulation arise from ignorance or careless use of little understood procedures, and some of the fundamental tools of the subject are much less well understood than commonly supposed. This is illustrated here by the saga of pseudorandom number generators, normal variate generators and the analysis of queueing system simulations. On the positive side, genuinely new uses of simulation are appearing, particularly in statistical inference. These are exemplified by recursive algorithms for simulating complex systems and simulation-based likelihood inference for point processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589392
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  • 5
    Electronic Resource
    Electronic Resource
    Experimental investigation of real-time scheduling in flexible manufacturing systems (1985)
    Springer
    Annals of operations research 3 (1985), S. 355-377 
    Details
    ISSN: 1572-9338
    Keywords: Flexible manufacturing systems ; scheduling ; manufacturing systems ; simulation ; computer integrated manufacturing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper presents a new two-phase (TP) approximate method for real-time scheduling in a flexible manufacturing system (FMS). This method combines a reduced enumeration schedule generation algorithm with a 0–1 optimization algorithm. In order to make the combined algorithm practicable, heuristic rules are introduced for the selection of jobs to be scheduled. The relative performance of the TP method vis-a-vis conventional heuristic dispatching rules such as SPT, LPT, FCFS, MWKR, and LWKR is investigated using combined process-interaction/discrete-event simulation models. An efficient experimental procedure is designed and implemented using these models, and the statistical analysis of the results is presented. For the particular case investigated, the conclusions are very encouraging. In terms of mean flow time, the TP method performs significantly better than any other tested heuristic dispatching rules. Also, the experimental results show that using global information significantly improves the FMS performance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02023749
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  • 6
    Electronic Resource
    Electronic Resource
    An overview of evaluative models for flexible manufacturing systems (1985)
    Springer
    Annals of operations research 3 (1985), S. 13-21 
    Details
    ISSN: 1572-9338
    Keywords: Flexible manufacturing systems ; queueing models ; simulation ; performance evaluation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Flexible manufacturing systems (FMSs) are a class of automated systems which can be used to improve productivity in discrete parts manufacturing. Due to the complexity of these systems, it is useful to have models that can aid in the design and operation of FMSs. We specifically differentiate here betweengenerative (or prescriptive) models, whichfind candidate decisions, andevaluative (or descriptive) models, whichevaluate a given set of decisions. We briefly cover, in a practical context, the pros and cons of these two classes of models. Then we focus on the latter class of models. Evaluative models for FMSs fall into five main classes, based on the technique used, namely: static allocation, queueing network theory, simulation, perturbation analysis, and Petri nets. Each of these approaches is briefly described, advantages and disadvantages mentioned, and references given to more detailed papers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02023766
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  • 7
    Electronic Resource
    Electronic Resource
    Probability theory versus simulation of petroleum potential in play analysis (1987)
    Springer
    Annals of operations research 8 (1987), S. 363-381 
    Details
    ISSN: 1572-9338
    Keywords: Probability ; simulation ; petroleum ; resources ; appraisal
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract An analytic probabilistic methodology for resource appraisal of undiscovered oil and gas resources in play analysis is presented. This play-analysis methodology is a geostochastic system for petroleum resource appraisal in explored as well as frontier areas. An objective was to replace an existing Monte Carlo simulation method in order to increase the efficiency of the appraisal process. Underlying the two methods is a single geologic model which considers both the uncertainty of the presence of the assessed hydrocarbon and its amount if present. The results of the model are resource estimates of crude oil, nonassociated gas, dissolved gas, and gas for a geologic play in terms of probability distributions. The analytic method is based upon conditional probability theory and a closed form solution of all means and standard deviations, along with the probabilities of occurrence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187102
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  • 8
    Electronic Resource
    Electronic Resource
    Integrated production scheduling in large-scale flexible electronic parts manufacturing (1988)
    Springer
    Annals of operations research 15 (1988), S. 269-287 
    Details
    ISSN: 1572-9338
    Keywords: Production scheduling ; integer programming ; simulation ; flexible manufacturing ; hierarchical modelling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This study reports the development of a production scheduling system for the integrated management of production in large-scale, high-volume electronic assembly lines. The development of the system incorporates control and planning considerations by addressing the interaction of various subsystems. Stochastic and deterministic aspects of the problem environment are appropriately handled via relevant simulation and analytic models. By effecting a hierarchical breakdown of the problem environment, the system produces information used in practical decision making for production planning and scheduling. Procedures used encompass and address considerations for management of work-in-process, optimization of the various subsystems' performance, minimization of setup time effect, and inventory carrying costs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186799
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  • 9
    Electronic Resource
    Electronic Resource
    A technique for on-line sensitivity analysis of flexible manufacturing systems (1985)
    Springer
    Annals of operations research 3 (1985), S. 379-391 
    Details
    ISSN: 1572-9338
    Keywords: Flexible manufacturing systems ; discrete event systems ; real-time systems ; monitoring ; simulation ; performance evaluation ; perturbation analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The recent perturbation analysis approach to discrete event systems is applied to flexible manufacturing systems (FMS). While analytic (queueing) models are useful in preliminary design of such systems, they are not accurate enough at the detailed design/operation stage. Thus, experimentation on detailed simulations or on the actual system has been the way to optimize system performance. Perturbation analysis allows us to derive the sensitivity of system performance, with respect to several design/operating parameters, by observing a single experiment (and without having to actually alter the parameters — often a costly operation). Thus, observation of one experiment can give accurate directions for the improvement of several parameter values. Here we give a simulation example illustrating how perturbation analysis could be used on-line on an FMS to improve its performance, including reducing its operating cost. Experimental results are also presented validating the estimates obtained from this technique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02023776
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  • 10
    Electronic Resource
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    Machine utilizations achieved using balanced FMS production ratios in a simulated setting (1988)
    Springer
    Annals of operations research 15 (1988), S. 227-267 
    Details
    ISSN: 1572-9338
    Keywords: FMS ; production ratios ; mathematical programming ; levels of detail in modeling ; balanced machine workloads ; machine utilizations ; dispatching rules ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Stecke [21] has developed mathematical programming approaches for determining, from a set of part type requirements, the production ratios (part types to be produced next, and their proportions) which maximize overall machine utilizations by balancing machine workloads in a flexible manufacturing system (FMS). These mathematical programming (MP) approaches are aggregate in the sense that they do not take into account such things as contention for transportation resources, travel time for work-in-process, contention for machines, finite buffer space, and dispatching rules. In the current study, the sensitivity of machine utilizations to these aggregations is investigated through simulation modeling. For the situation examined, it is found that achieved machine utilizations are a strong function of some of the factors ignored in the MP methodology, ranging from 9.1% to 22.9% less than those theoretically attainable under the mathematical programming assumptions. The 9.1% degradation results from modeling with nonzero work-in-process travel times (i.e. 2 minutes per transfer) and using only central work-in-process buffers. Resource levels (e.g. the number of automated guided vehicles; the amount of work-in-process; the number of slack buffers) needed to limit the degradation to 9.1% correspond to FMS operating conditions which are feasible in practice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186798
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  • 11
    Electronic Resource
    Electronic Resource
    Monte carlo estimation of the sampling distribution of nonlinear model parameter estimators (1987)
    Springer
    Annals of operations research 8 (1987), S. 243-256 
    Details
    ISSN: 1572-9338
    Keywords: Control variates ; Monte Carlo ; nonlinear estimation ; simulation ; variance reduction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The sampling distribution of parameter estimators can be summarized by moments, fractiles or quantiles. For nonlinear models, these quantities are often approximated by power series, approximated by transformed systems, or estimated by Monte Carlo sampling. A control variate approach based on a linear approximation of the nonlinear model is introduced here to reduce the Monte Carlo sampling necessary to achieve a given accuracy. The particular linear approximation chosen has several advantages: its moments and other properties are known, it is easy to implement, and there is a correspondence to asymptotic results that permits assessment of control variate effectiveness prior to sampling via measures of nonlinearity. Empirical results for several nonlinear problems are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187095
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  • 12
    Electronic Resource
    Electronic Resource
    Response surface methodology as a means for efficient data storage and retrieval (1987)
    Springer
    Annals of operations research 8 (1987), S. 351-362 
    Details
    ISSN: 1572-9338
    Keywords: Response surface methodology ; simulation ; optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Managing the volume of experimental and/or simulation data required for large-scale design studies can be a significant problem. This paper describes a method for dealing with this problem, using response surface methodology. The method involves (1) determining a summary parameterization of the response of the underlying process mechanism generating the data, in order to characterize this response in terms of a manageable set of performance measures, and (2) deriving a model of the data, in order to summarize the dependence of the performance measures on selected predictor or design variables. The method is illustrated by its application to a problem in vehicle collision research.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187101
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  • 13
    Electronic Resource
    Electronic Resource
    The alternate-block-factorization procedure for systems of partial differential equations (1989)
    Springer
    BIT 29 (1989), S. 938-954 
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    ISSN: 1572-9125
    Keywords: 65F10 ; Semiconductors ; simulation ; partial differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The alternate-block-factorization (ABF) method is a procedure for partially decoupling systems of elliptic partial differential equations by means of a carefully chosen change of variables. By decoupling we mean that the ABF strategy attempts to reduce intra-equation coupling in the system rather than intra-grid coupling for a single elliptic equation in the system. This has the effect of speeding convergence of commonly used iteration schemes, which use the solution of a sequence of linear elliptic PDEs as their main computational step. Algebraically, the change of variables is equivalent to a postconditioning of the original system. The results of using ABF postconditioning on some problems arising from semiconductor device simulation are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01932753
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  • 14
    Electronic Resource
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    Uniformly distributed sums of bernoulli variables (1988)
    Springer
    BIT 28 (1988), S. 671-677 
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    ISSN: 1572-9125
    Keywords: I.6.1 ; I.6.3 ; simulation ; Bernoulli ; binomial ; uniform sums ; 0–1 arrays
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Sums of independent, identically distributed (iid) binomial variates have binomial distributions; yet it is possible to construct a sequence of binomial distributions over {0, 1} for variatesX 1,X 2, ... such that all partial sumsY i =X 1 + ... +X i have uniform distributions. The price to pay is to give up the iid condition. Requiring the property of only one sum does not alleviate the situation much. It is also possible to generate on a computerm × n-matrices, of 0–1 binomial variates with uniformly distributed row and column sums of all major submatrices, but only for smallm andn. Even a three-dimensional 2 × 2 × 2 array can have a similar property. Other target distributions than the rectangular are possible, but cumbersome. An example with smaller variance is given. The results were needed for simulating the performance of some Operations Research algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01941142
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  • 15
    Electronic Resource
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    A simulation tool for the performance evaluation of parallel branch and bound algorithms (1988)
    Springer
    Mathematical programming 42 (1988), S. 245-271 
    Details
    ISSN: 1436-4646
    Keywords: 90C27 ; 68Q10 ; 68R05 ; Parallel computer ; MIMD ; branch and bound ; nondeterminism ; asynchronicity ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Parallel computation offers a challenging opportunity to speed up the time consuming enumerative procedures that are necessary to solve hard combinatorial problems. Theoretical analysis of such a parallel branch and bound algorithm is very hard and empirical analysis is not straightforward because the performance of a parallel algorithm cannot be evaluated simply by executing the algorithm on a few parallel systems. Among the difficulties encountered are the noise produced by other users on the system, the limited variation in parallelism (the number of processors in the system is strictly bounded) and the waste of resources involved: most of the time, the outcomes of all computations are already known and the only issue of interest is when these outcomes are produced. We will describe a way to simulate the execution of parallel branch and bound algorithms on arbitrary parallel systems in such a way that the memory and cpu requirements are very reasonable. The use of simulation has only minor consequences for the formulation of the algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589406
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  • 16
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    A mathematician's journey through operational research (1988)
    Springer
    Mathematical programming 42 (1988), S. 33-40 
    Details
    ISSN: 1436-4646
    Keywords: Decision theory ; mathematical modelling ; operational research ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589390
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  • 17
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    Pontryagin's principle for control problems in age-dependent population dynamics (1985)
    Springer
    Journal of mathematical biology 23 (1985), S. 75-101 
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    ISSN: 1432-1416
    Keywords: Population dynamics ; Optimal harvesting ; Optimal control ; Hyperbolic systems ; Pontryagin's principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper, Pontryagin's principle is proved for a fairly general problem of optimal control of populations with continuous time and age variable. As a consequence, maximum principles are developed for an optimal harvesting problem and a problem of optimal birth control.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276559
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  • 18
    Electronic Resource
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    Spectral-type simulation of spatially correlated fracture set properties (1985)
    Springer
    Mathematical geology 17 (1985), S. 41-52 
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    ISSN: 1573-8868
    Keywords: fracture set ; simulation ; spectral density ; Fourier transform
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Fracture set properties such as orientation, spacing, trace length, and waviness tend to be spatially correlated. These properties can be efficiently simulated by spectral analysis procedures that take advantage of the computational speed of the fast Fourier transform. The covariance function of each property to be simulated is obtained from the variogram function estimated from mapped fracture set data and is typically referenced to the mean vector of the set. Simulation procedures for normally and exponentially distributed data involve generating uncorrelated Fourier coefficients that are assigned proper variance according to the spectral density, which is the Fourier transform of the covariance function. These coefficients are then reverse Fourier transformed to produce simulated set properties that have the desired variance and variogram function.
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    URL: http://dx.doi.org/10.1007/BF01030366
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  • 19
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    Two-dimensional simulation by turning bands (1985)
    Springer
    Mathematical geology 17 (1985), S. 81-90 
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    ISSN: 1573-8868
    Keywords: simulation ; turning bands ; covariance ; semivariogram ; geostatistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Journel (1974) developed the turning-bands method which allows a three-dimensional data set with specified covariance to be obtained by the simulation of several one-dimensional realizations which have an intermediate covariance. The relationship between the threedimensional and one-dimensional covariance is straightforward and allows the one-dimensional covariance to be obtained immediately. In theory a dense uniform distribution of lines in three-dimensional space is required along which the one-dimensional realizations are generated; in practice most workers have been content to use the fifteen axes of the regular icosahedron. Many mining problems may be treated in two dimensions, and in this paper a turning-bands approach is developed to generate two-dimensional data sets with a specified covariance. By working in two dimensions, the area on which the data is simulated may be divided as finely as desired by the lines on which the one-dimensional realizations are first generated. The relationship between the two-dimensional and one-dimensional covariance is derived as a nontrivial integral equation. This is solved analytically for the onedimensional covariance. The method is applied to the generation of a two-dimensional data set with spherical covariance.
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    URL: http://dx.doi.org/10.1007/BF01030369
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  • 20
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    The Bi-Gaussian approach: A simple method for recovery estimation (1985)
    Springer
    Mathematical geology 17 (1985), S. 625-644 
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    ISSN: 1573-8868
    Keywords: recoveries ; multi-Gaussian ; bi-Gaussian ; simulation ; disjunctive kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A new and simple method is proposed to obtain estimates of recovery functions: the Bi-Gaussian approach. Existing methods estimate recovery functions with conditional distributions where the conditioning set is all the data available. Here instead the simple kriging estimate of the Gaussian transform is proposed to be used. Results in the point recovery case are identical to the multi-Gaussian approach of Verly (1983, 1984), whereas in the non-point-support situation, an approximation is derived which saves computer time as compared to employing the strict multi-Gaussian hypothesis. Two examples compare favorably with the well-established disjunctive kriging method (discrete Gaussian model).
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    URL: http://dx.doi.org/10.1007/BF01030857
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  • 21
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    Generating large stochastic simulations—The matrix polynomial approximation method (1987)
    Springer
    Mathematical geology 19 (1987), S. 99-107 
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    ISSN: 1573-8868
    Keywords: geostatistics ; simulation ; Toeplitz matrices ; block Toeplitz matrices ; matrix polynomial approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An algorithm for producing a nonconditional simulation by multiplying the square root of the covariance matrix by a random vector is described. First, the square root of a matrix (or a function of a matrix in general) is defined. The square root of the matrix can be approximated by a minimax matrix polynomial. The block Toeplitz structure of the covariance matrix is used to minimize storage. Finally, multiplication of the block Toeplitz matrix by the random vector can be evaluated as a convolution using the fast Fourier transform. This results in an algorithm which is not only efficient in terms of storage and computation but also easy to implement.
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    URL: http://dx.doi.org/10.1007/BF00898190
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  • 22
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    Nonlinear dynamics in a complex cubic one-dimensional model for sensory psychophysics (1988)
    Springer
    Acta applicandae mathematicae 11 (1988), S. 1-17 
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    ISSN: 1572-9036
    Keywords: 92 (30E) ; Psychophysics ; sensory noise ; chaos ; feedforward processes ; simulation ; nonlinear modelling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A cubic recursion with complex variable, has different properties in the phase spases of the reals and the imaginaries. The separation of the dynamics of the parts may be interpretable in terms of sensory intensity signal transmission through higher neural networks in man.
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    URL: http://dx.doi.org/10.1007/BF00047112
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  • 23
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    Applications of the mathematical model of immunological tolerance to immunoglobulin suppression and AIDS (1989)
    Springer
    Acta applicandae mathematicae 14 (1989), S. 135-142 
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    ISSN: 1572-9036
    Keywords: 92A07 ; immune system ; modelling ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046680
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  • 24
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    Interleukin 2 and immune response control mathematical model (1989)
    Springer
    Acta applicandae mathematicae 14 (1989), S. 179-189 
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    ISSN: 1572-9036
    Keywords: 92A07 ; immune response ; ordinary differential equations ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046684
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  • 25
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    Mathematical simulation of the immunomodulating role of energy metabolism in support of synergism and antagonism of the compartments of an immune system (1989)
    Springer
    Acta applicandae mathematicae 14 (1989), S. 167-178 
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    ISSN: 1572-9036
    Keywords: 92A07 ; immune response ; metabolism ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
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    Regional environmental simulation of African cattle herding societies (1986)
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    Human ecology 14 (1986), S. 117-130 
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    ISSN: 1572-9915
    Keywords: regional ; East Africa ; cattle ; simulation ; food supply
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Energy, Environment Protection, Nuclear Power Engineering , Ethnic Sciences
    Notes: Abstract Regional analyses of the interaction between human populations and natural resources must integrate landscape scale environmental problems. An approach that considers human culture, environmental processes, and resource needs offers an appropriate methodology. With this methodology, we analyze problems of food availability in African cattle-keeping societies. The analysis interrelates cattle biomass, forage availability, milk and blood production, crop yields, gathering, food subsidies, population, and variable precipitation. While an excess of cattle leads to overgrazing, cattle also serve as valuable food storage mechanisms during low rainfall periods. Food subsidies support higher population levels but do not alter drought-induced population fluctuations. Variable precipitation patterns require solutions that stabilize year-to-year food production and also address problems of overpopulation.
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    Existence of an optimal control with sparse jumps in the state variable (1985)
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    Journal of optimization theory and applications 45 (1985), S. 265-293 
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    ISSN: 1573-2878
    Keywords: Optimal control ; control differential systems involving impulses ; jumps in the state variables
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The existence of an optimal control is proved in a problem where the criterion functional and the equation of motion contain a control that is a Lebesgue-Stieltjes measure. Due to nonlinearities in the problem, it is necessary to postulate a condition implying that large atoms of the control measures are sparse and that their derivatives, wherever they exist, have a uniform bound.
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    A class of nondifferentiable control problems (1988)
    Springer
    Journal of optimization theory and applications 56 (1988), S. 227-243 
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    ISSN: 1573-2878
    Keywords: Optimal control ; nondifferentiable control problems ; optimality conditions ; Fritz John optimality conditions ; duality ; converse duality ; continuous programming ; mathematical programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Optimality conditions and duality results are obtained for a class of control problems having a nondifferentiable term in the integrand of the objective functional. These results generalize many well-known results in optimal control theory involving differentiable functions, and also provide a relationship with certain nondifferentiable mathematical programming problems. Some extensions concerning the unified treatment of optimal control theory and continuous programming are also mentioned. Finally, a control problem containing an arbitrary norm, along with its appropriate norm, is given.
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    Differential sensitivity of solutions of convex constrained optimal control problems for discrete systems (1987)
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    Journal of optimization theory and applications 53 (1987), S. 429-449 
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    ISSN: 1573-2878
    Keywords: Optimal control ; discrete systems ; convex problems ; state and control constraints ; sensitivity analysis ; right-differentiability with respect to a parameter
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A family of optimal control problems for discrete systems that depend on a real parameter is considered. The problems are strongly convex and subject to state and control constraints. Some regularity conditions are imposed on the constraints. The control problems are reformulated as mathematical programming problems. It is shown that both the primal and dual optimal variables for these problems are right-differentiable functions of a parameter. The right-derivatives are characterized as solutions to auxiliary quadratic control problems. Conditions of continuous differentiability are discussed, and some estimates of the rate of convergence of the difference quotients to the respective derivatives are given.
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    Decentralized optimum load frequency control of interconnected power systems (1985)
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    Journal of optimization theory and applications 45 (1985), S. 517-531 
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    ISSN: 1573-2878
    Keywords: Optimal control ; parameter optimization ; power systems ; load frequency control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new approach for designing a linear regulator for the problem of load frequency control (LFC) of interconnected power systems is developed. The control is specified to be of proportional-plus-integral (P-I) form and is only a function of the measurable states. The LFC problem is formulated as a parameter optimization problem.
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    On the optimality of the logistic growth (1988)
    Springer
    Journal of optimization theory and applications 57 (1988), S. 513-517 
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    ISSN: 1573-2878
    Keywords: Optimal control ; population growth ; logistic equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The rate at which a population should grow is determined by finding the best trade-off between the loss due to the deviation from a target population size and the loss associated to the growing effort. It is also shown that, in the case of infinite-time horizon and quadratic loss functions, the optimal growth is logistic.
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    On the use of Hamiltonian and maximized Hamiltonian in nondifferentiable control theory (1985)
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    Journal of optimization theory and applications 46 (1985), S. 493-504 
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    ISSN: 1573-2878
    Keywords: Optimal control ; envelope theorem ; differential inclusions ; nondifferentiable functions ; production-employment model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In optimal control problems involving nondifferentiable functions of the state variable, the adjoint differential inclusion can be formulated by either use of the Hamiltonian or the maximized Hamiltonian. In this paper, we solve a production-employment model in which the latter approach must be utilized, since the former does not enable one to determine the optimal policy.
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    Control problems with random and progressively known targets (1988)
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    Journal of optimization theory and applications 59 (1988), S. 445-465 
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    ISSN: 1573-2878
    Keywords: Optimal control ; linear-quadratic systems ; unknown targets ; points of information
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The situation considered is of optimally controlling a deterministic system from a given state to an initially unknown targety in a fixed time interval [T 0,T]. The target will be certainly known at a random time τ in [T 0,T]. The controller knows the distributions ofy and τ. We derive the Bellman equation for the problem, prove a verification theorem for it, and demonstrate how the distribution τ influences the optimal control. We show that, in the linear-quadratic case, the optimal control is given by a feedback law that does not depend on the distribution of τ.
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    Numerical approximation of nonconvex optimal control problems defined by parabolic equations (1985)
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    Journal of optimization theory and applications 45 (1985), S. 73-88 
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    ISSN: 1573-2878
    Keywords: Optimal control ; nonconvexity ; relaxed controls ; parabolic systems ; relaxed minimum principle ; approximations ; descent methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider an optimal control problem for distributed systems governed by parabolic equations. The state equations are nonlinear in the control variable; the constraints and the cost functional are generally nonconvex. Relaxed controls are used to prove existence and derive necessary conditions for optimality. To compute optimal controls, a descent method is applied to the resulting relaxed problem. A numerical method is also given for approximating a special class of relaxed controls, notably those obtained by the descent method. Convergence proofs are given for both methods, and a numerical example is provided.
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    Optimal load frequency control with governor backlash (1985)
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    Journal of optimization theory and applications 45 (1985), S. 505-516 
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    ISSN: 1573-2878
    Keywords: Optimal control ; parameter optimization ; power systems ; load frequency control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new technique is described for designing an optimal controller for a system whose dynamical equations contain a backlash element. The approach is applied to the problem of load frequency control (LFC) of a single area steam power system.
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    Uniformly valid feedback expansions for optimal control of singularly perturbed dynamic systems (1985)
    Springer
    Journal of optimization theory and applications 46 (1985), S. 441-453 
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    ISSN: 1573-2878
    Keywords: Optimal control ; singular perturbations ; autonomous systems ; feedback control ; Hamilton-Jacobi-Bellmann equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper shows how to construct a feedback control law for a class of singularly perturbed autonomous optimization problems. The control law is expressed as a single power series in the small parameter ∈ representing the ratio of the two effective time scales of the problem. The present approach avoids the need of expansion matching. The method is applied to a constant-speed interception problem. Comparison of numerical results with the exact solution shows an excellent agreement.
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    Closed-form solutions for a class of optimal quadratic tracking problems (1985)
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    Journal of optimization theory and applications 47 (1985), S. 465-481 
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    ISSN: 1573-2878
    Keywords: Optimal control ; tracking systems ; computational methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Closed-from solutions are derived for a class of tracking problems including a linear optimal regulator and a prefilter for a time-invariant plant. The solutions for the prefilter equation and state trajectory, coupled by the Riccati equation, are exponentially related to the stability matrix of the plant. A computational procedure is presented in recursive form when the desired output state dynamics is assumed linear and time-invariant. Several examples are given for illustration.
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    A Carathéodory-Hamilton-Jacobi theory for infinite-horizon optimal control problems (1986)
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    Journal of optimization theory and applications 48 (1986), S. 265-287 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Hamilton-Jacobi theory ; infinite horizon ; equivalent variational problems
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    Topics: Mathematics
    Notes: Abstract In this paper, we extend Carathéodory's concept of equivalent variational problems to infinite-horizon optimal control problems. In such a setting, the usual concept of a minimum need not exist, and we therefore consider a weaker definition of optimality, known as catching up optimality. The extension presented here leads us to a Hamilton-Jacobi theory for infinite-horizon optimal control problems that closely parallels the classical work of Carathéodory as well as providing sufficient conditions for optimality. Finally, we show that the results given here subsume several previously known results as a special case.
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    An optimal control problem in the study of liver kinetics (1986)
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    Journal of optimization theory and applications 48 (1986), S. 289-302 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Pontryagin's maximum principle ; optimization of liver kinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The enzyme activities in the liver are described by a system of ordinary differential equations. A certain substance in the blood is transformed twice by different kinds of enzymes. The mathematical problem is to determine the distribution of the enzymes along the blood flow so that the outflow concentration of the once-transformed form of the substance is as small as possible. This problem has been considered before and solved for particular types of enzyme kinetics. In this paper, we solve the problem for more general types of kinetics (including substrate- inhibition kinetics). The methods used are also different, in that the problem is considered as a problem of optimal control and Pontryagin's maximum principle is applied to derive necessary conditions.
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    On the existence of catching-up optimal solutions for Lagrange problems defined on unbounded intervals (1986)
    Springer
    Journal of optimization theory and applications 49 (1986), S. 207-225 
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    ISSN: 1573-2878
    Keywords: Optimal control ; existence theory ; catching-up optimal solutions ; infinite-horizon problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we are concerned with the question of the existence of optimal solutions for infinite-horizon optimal control problems of Lagrange type. In such problems, the objective or cost functional is described by an improper integral. As dictated by applications arising in mathematical economics, we do nota priori assume that this improper integral converges. This leads us to consider a weaker type of optimality, known as catching-up optimality. The results presented here utilize the classical convexity and seminormality conditions typically imposed in the existence theory for the case of finite intervals. These conditions are significantly weaker than those imposed by other authors; as a consequence, their existence results are contained as special cases of the results presented here. The method of proof utilizes the Carathéodory-Hamilton-Jacobi theory previously developed by the author for infinite-horizon optimal control problems.
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    Optimal operation of multireservoir power systems (1986)
    Springer
    Journal of optimization theory and applications 49 (1986), S. 449-461 
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    ISSN: 1573-2878
    Keywords: Optimal control ; multireservoir hydroelectric power systems ; optimal release policies ; series reservoirs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The optimal monthly operating policy of a multireservoir hydroelectric power system is a stochastic nonlinear problem. This paper presents a new method for determining the optimal monthly operating policy of a power system ofn reservoirs in series on a river taking into account the stochasticity of the river flows. Functional optimization techniques and minimum-norm formulation have been used to find the optimal release policy of the system. Results for a numerical example composed of four reservoirs are presented.
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    Long-term optimal operation of a parallel multireservoir power system (1986)
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    Journal of optimization theory and applications 50 (1986), S. 383-395 
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    ISSN: 1573-2878
    Keywords: Optimal control ; multireservoir hydroelectric power systems ; optimal release policy ; parallel reservoirs
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    Topics: Mathematics
    Notes: Abstract Long-term optimal operation of a multireservoir system is complex because it is a dynamic problem (present decisions for one reservoir depend on future decisions for all reservoirs); the optimal operating policy for one reservoir depends not only on its own energy content, but also on the corresponding content of each one of the other reservoirs; it is a highly stochastic problem with respect to the reservoir inflows and it is a nonlinear problem. This paper presents a new method for determining the optimal monthly operating policy of a power system consisting of multireservoirs on a multiriver system taking into account the stochasticity of the river flows. Functional optimization techniques and minimum norm formulation have been used. Results for a numerical example composed of three rivers with four reservoirs, three reservoirs, and two reservoirs on each river, respectively, are presented.
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    Modelling and optimization of reservoirs for long-term regulation with variable head using functional analysis (1986)
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    Journal of optimization theory and applications 50 (1986), S. 463-477 
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    ISSN: 1573-2878
    Keywords: Optimal control ; multireservoir hydroelectric power system ; optimal release policy ; variable head ; functional analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, functional analysis and minimum norm formulation are applied to maximize the total benefits from two hydro reservoirs. The hydroelectric power generation is treated as a nonlinear function; water head variation and stochasticity of the river flows are included. The resulting problem has a nonlinear objective function and linear constraints. The proposed method is computationally efficient, compared to previous techniques. Numerical results are presented for widely different water conditions for an actual system in operation.
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    Existence of finitely optimal solutions for infinite-horizon optimal control problems (1986)
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    Journal of optimization theory and applications 51 (1986), S. 41-62 
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    ISSN: 1573-2878
    Keywords: Optimal control ; existence theory ; finite optimality ; infinite horizons ; continuous dependence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we investigate the existence of finitely optimal solutions for the Lagrange problem of optimal control defined on [0, ∞) under weaker convexity and seminormality hypotheses than those of previous authors. The notion of finite optimality has been introduced into the literature as the weakest of a hierarchy of types of optimality that have been defined to permit the study of Lagrange problems, arising in mathematical economics, whose cost functions either diverge or are not bounded below. Our method of proof requires us to analyze the continuous dependence of finite-interval Lagrange problems with respect to a prescribed terminal condition. Once this is done, we show that a finitely optimal solution can be obtained as the limit of a sequence of solutions to a sequence of corresponding finite-horizon optimal control problems. Our results utilize the convexity and seminormality hypotheses which are now classical in the existence theory of optimal control.
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    Closed-form recursive formula for an optimal tracker with terminal constraints (1986)
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    Journal of optimization theory and applications 51 (1986), S. 307-320 
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    ISSN: 1573-2878
    Keywords: Optimal control ; tracking systems ; computational methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. An example involving the feedback slewing of a flexible spacecraft is given to illustrate the validity and usefulness of the formulations.
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    A noniterative algebraic solution for Riccati equations satisfying two-point boundary-value problems (1986)
    Springer
    Journal of optimization theory and applications 51 (1986), S. 355-362 
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    ISSN: 1573-2878
    Keywords: Optimal control ; piecewise periodic feedback gains ; two-point boundary-value problems ; continuous-time Riccati equation ; discrete-time Riccati equation ; continuous-time Lyapunov equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A noniterative algebraic method is presented for solving differential Riccati equations which satisfy two-point boundary-value problems. This class of numerical problems arises in quadratic optimization problems where the cost functionals are composed of both continuous and discrete state penalties, leading to piecewise periodic feedback gains. The necessary condition defining the solution for the two-point boundary value problem is cast in the form of a discrete-time algebraic Riccati equation, by using a formal representation for the solution of the differential Riccati equation. A numerical example is presented which demonstrates the validity of the approach.
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    Finding candidate singular optimal controls: A state of the art survey (1989)
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    Journal of optimization theory and applications 60 (1989), S. 173-190 
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    ISSN: 1573-2878
    Keywords: Optimal control ; singular control ; singular control order
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Pontryagin's maximum principle gives no information about a singular optimal control if the problem is linear. This survey shows how candidate singular optimal controls may be found for linear and nonlinear problems. A theorem is given on the maximum order of a linear singular problem.
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    A new technique for linear static state estimation based on weighted least absolute value approximations (1989)
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    Journal of optimization theory and applications 61 (1989), S. 123-136 
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    ISSN: 1573-2878
    Keywords: Optimal control ; linear estimation ; state estimation ; least absolute value ; optimal estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a new technique for solving the problem of linear static state estimation, based on weighted least absolute value (WLAV). A set ofm optimality equations is obtained, wherem=number of measurements, based on minimizing a WLAV performance index involvingn unknown state variables,m〉n. These equations are solved using the left pseudo-inverse transformation, least-square sense, to obtain approximately the residual of each measurement. Ifk is the rank of the matrixH,k=n, we choose among the optimality equations a number of equations equal to the rankk and having the smallest residuals. The solution of thesen equations inn unknowns yields the best WLAV estimation. A numerical example is reported; the results for this example are obtained by using both WLS and WLAV techniques. It is shown that the best WLAV approximation is superior to the best WLS approximation when estimating the true form of data containing some inaccurate observations.
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    Linear quadratic optimal control for discrete descriptor systems (1989)
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    Journal of optimization theory and applications 61 (1989), S. 221-245 
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    Keywords: Optimal control ; descriptor systems ; singular systems ; discrete systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The present paper deals with the investigation of the linear quadratic optimal control problem for the discrete-time descriptor systemsEx k+1=Ax k +Bu k , whereE is in general a singular matrix and the system structure is in general noncausal. The problem is considered in its general form, having singular cost matrices and cross-weighting term in the cost functional. The key idea for the solution approach is the use of the Weierstrass theorem for regular pencils, combined with a suitable permutation transformation, to form a base for the image ofE. The optimization problem is solved by forcing causality to the Hamiltonian equations, which are produced by considering the entireN-stage process as a large system of linear equations. The feedback gain matrix is obtained as a manifold which is generated by the intersection of two other manifolds.
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    Minimal trajectories of nonconvex differential inclusions (1989)
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    Journal of optimization theory and applications 61 (1989), S. 359-376 
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    ISSN: 1573-2878
    Keywords: Optimal control ; nonconvex differential inclusions ; endpoint constraints ; maximum principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider an optimization problem with endpoint constraints associated with a nonconvex differential inclusion. We give a necessary condition of the maximum principle type for a solution of the problem. Following the approach from Ref. 1, the condition is stated in terms of single-valued selections of the convexified right-hand side of the inclusion.
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    Sufficient optimality conditions for nonconvex control problems with state constraints (1989)
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    Journal of optimization theory and applications 62 (1989), S. 289-310 
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    ISSN: 1573-2878
    Keywords: Optimal control ; sufficient conditions ; state constraints ; nonconvex optimization
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract The sufficient optimality conditions of Zeidan for optimal control problems (Refs. 1 and 2) are generalized such that they are applicable to problems with pure state-variable inequality constraints. We derive conditions which neither assume the concavity of the Hamiltonian nor the quasiconcavity of the constraints. Global as well as local optimality conditions are presented.
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    A solution method for regular optimal control problems with state constraints (1989)
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    Journal of optimization theory and applications 62 (1989), S. 489-513 
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    Keywords: Optimal control ; regular problems ; state constraints ; method of region analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A method of region analysis is developed for solving a class of optimal control problems with one state and one control variable, including state and control constraints. The performance index is strictly convex with respect to the control variable, while this variable appears only linearly in the state equation. The convexity or linearity assumption of the performance index or the state equation with respect to the state variable is not required.
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    Nonlinear optimal control problems with continuous state inequality constraints (1989)
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    Journal of optimization theory and applications 63 (1989), S. 1-22 
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    ISSN: 1573-2878
    Keywords: Optimal control ; continuous inequality state constraints ; computational algorithms ; control parametrization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of optimal control problems involving continuous inequality state constraints. This class of optimal control problems can be solved using the technique developed in a paper by Goh and Teo, where a simple constraint transcription is used to convert continuous inequality state constraints into equivalent equality terminal state constraints. However, that constraint transcription has the disadvantage that the equality terminal state constraints so obtained do not satisfy the usual constraint qualification. Thus, convergence is not guaranteed and some oscillation may exist in numerical computation. The aim of this paper is to use a new constraint transcription together with the concept of control parametrization to devise a new computational algorithm for solving this general class of constrained optimal control problems. This new algorithm is much more stable numerically, as we have successfully overcome the above-mentioned disadvantages.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940727
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    On the existence of sporadically catching-up optimal solutions for infinite-horizon optimal control problems (1987)
    Springer
    Journal of optimization theory and applications 53 (1987), S. 219-235 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; existence theory ; sporadically catching-up optimality ; infinite-horizon optimal control problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we extend the existence theory of Brock and Haurie concerning the existence of sporadically catching-up optimal solutions for autonomous, infinite-horizon optimal control problems. This notion of optimality is one of a hierarchy of types of optimality that have appeared in the literature to deal with optimal control problems whose cost functionals, described by an improper integral, either diverge or are unbounded below. Our results rely on the now classical convexity and seminormality hypotheses due to Cesari and are weaker than those assumed in the work of Brock and Haurie. An example is presented where our results are applicable, but those of the above-mentioned authors do not.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939215
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  • 55
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    A new sufficient condition for most rapid approach paths (1987)
    Springer
    Journal of optimization theory and applications 54 (1987), S. 403-411 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Green's theorem method ; infinite-horizon problems ; most rapid approach
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we show that in some previous literature the most rapid approach theorems are incomplete. This is proved by providing a counterexample. We also introduce an additional condition that guarantees the optimality of the most rapid approach path.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939441
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  • 56
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    Local convergence of an algorithm for solving optimal control problems (1985)
    Springer
    Journal of optimization theory and applications 46 (1985), S. 265-293 
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    ISSN: 1573-2878
    Keywords: Optimal control ; terminal equality constraints ; multiplier methods ; augmented Lagrangians ; linearly convergent update formulas
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, a method is proposed for the numerical solution of optimal control problems with terminal equality constraints. The multiplier method is employed to deal with the terminal equality constraints. It is shown that a sequence of control functions, which converges to the optimal control, is obtained by the alternate update of control functions and multipliers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939285
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  • 57
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    Simulation of the movement and dispersion of oil slicks in the Arabian Gulf (1988)
    Springer
    Natural hazards 1 (1988), S. 197-219 
    Details
    ISSN: 1573-0840
    Keywords: Arabian Gulf ; oil ; oil ; simulation ; meteorology ; tides ; residual currents
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The extensive oil drilling and transportation activities in the Arabian Gulf increased the possibility of oil spills and the consequent threat of oil pollution to the regional ecology. The available literature concerning the main aspects of the physical oceanographic characteristics affecting the movement and spreading of oil spill in the Gulf are reviewed. It is concluded that evaporation, wind-driven currents, and sandfall are important as weathering processes, while tidal currents cause lateral spreading of the slick. Oil spill modelling has shown some usefulness in estimating the trajectories of few major spills illustrated by reference to three models developed for the Gulf. The performance of these models, their capabilities and limitations are reviewed. Recommendations are made to gather more data on the behavior of oil spills in this particular environment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00126615
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  • 58
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    Real-time application of an oil spill movement prediction system (1989)
    Springer
    Natural hazards 2 (1989), S. 31-44 
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    ISSN: 1573-0840
    Keywords: Oil spill ; pollution ; simulation ; Canada ; emergency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper deals with the prediction, in real time, of the motion of experimental oil slicks. The experiments were conducted during September 1983 offshore near Halifax on the east coast of Canada. The objectives of the experiments were (i) to determine the suitability of oil spill dispersants as countermeasures and (ii) the testing and verification of oil spill trajectory models and systems. The Atmospheric Environment Service (AES) participated in the experiments to test the capability of its oil spill motion prediction system in providing real-time trajectory forecasts. The experiment consisted of three sets of spills. Each set had a control slick and a test slick. Sixteen barrels of crude oil were used in each spill. The test slicks were used to test the effectiveness of various dispersants, the control slicks were used to verify trajectory forecasts. The spill trajectories and oil weathering information obtained from the system during the experiments demonstrated the relative ease with which the system could handle the required input and provide timely forecasts. The accuracy of these forecast trajectories was confirmed by observations, and their utility was demonstrated by their application in the operational decision-making process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00124756
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