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  • Articles  (31)
  • Optimal control  (31)
  • 1985-1989  (31)
  • Mathematics  (31)
  • Energy, Environment Protection, Nuclear Power Engineering
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  • Articles  (31)
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  • 1
    Electronic Resource
    Electronic Resource
    Pontryagin's principle for control problems in age-dependent population dynamics (1985)
    Springer
    Journal of mathematical biology 23 (1985), S. 75-101 
    Details
    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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  • 2
    Electronic Resource
    Electronic Resource
    Existence of an optimal control with sparse jumps in the state variable (1985)
    Springer
    Journal of optimization theory and applications 45 (1985), S. 265-293 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939981
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  • 3
    Electronic Resource
    Electronic Resource
    A class of nondifferentiable control problems (1988)
    Springer
    Journal of optimization theory and applications 56 (1988), S. 227-243 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939409
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  • 4
    Electronic Resource
    Electronic Resource
    Differential sensitivity of solutions of convex constrained optimal control problems for discrete systems (1987)
    Springer
    Journal of optimization theory and applications 53 (1987), S. 429-449 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938948
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  • 5
    Electronic Resource
    Electronic Resource
    Decentralized optimum load frequency control of interconnected power systems (1985)
    Springer
    Journal of optimization theory and applications 45 (1985), S. 517-531 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939132
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  • 6
    Electronic Resource
    Electronic Resource
    On the optimality of the logistic growth (1988)
    Springer
    Journal of optimization theory and applications 57 (1988), S. 513-517 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02346168
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  • 7
    Electronic Resource
    Electronic Resource
    On the use of Hamiltonian and maximized Hamiltonian in nondifferentiable control theory (1985)
    Springer
    Journal of optimization theory and applications 46 (1985), S. 493-504 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939154
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  • 8
    Electronic Resource
    Electronic Resource
    Control problems with random and progressively known targets (1988)
    Springer
    Journal of optimization theory and applications 59 (1988), S. 445-465 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940309
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  • 9
    Electronic Resource
    Electronic Resource
    Numerical approximation of nonconvex optimal control problems defined by parabolic equations (1985)
    Springer
    Journal of optimization theory and applications 45 (1985), S. 73-88 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940814
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  • 10
    Electronic Resource
    Electronic Resource
    Optimal load frequency control with governor backlash (1985)
    Springer
    Journal of optimization theory and applications 45 (1985), S. 505-516 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939131
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  • 11
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939149
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  • 12
    Electronic Resource
    Electronic Resource
    Closed-form solutions for a class of optimal quadratic tracking problems (1985)
    Springer
    Journal of optimization theory and applications 47 (1985), S. 465-481 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00942192
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  • 13
    Electronic Resource
    Electronic Resource
    A Carathéodory-Hamilton-Jacobi theory for infinite-horizon optimal control problems (1986)
    Springer
    Journal of optimization theory and applications 48 (1986), S. 265-287 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; Hamilton-Jacobi theory ; infinite horizon ; equivalent variational problems
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940673
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  • 14
    Electronic Resource
    Electronic Resource
    An optimal control problem in the study of liver kinetics (1986)
    Springer
    Journal of optimization theory and applications 48 (1986), S. 289-302 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940674
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  • 15
    Electronic Resource
    Electronic Resource
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940757
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  • 16
    Electronic Resource
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    Optimal operation of multireservoir power systems (1986)
    Springer
    Journal of optimization theory and applications 49 (1986), S. 449-461 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00941072
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  • 17
    Electronic Resource
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    Long-term optimal operation of a parallel multireservoir power system (1986)
    Springer
    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
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938626
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  • 18
    Electronic Resource
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    Modelling and optimization of reservoirs for long-term regulation with variable head using functional analysis (1986)
    Springer
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938632
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  • 19
    Electronic Resource
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    Existence of finitely optimal solutions for infinite-horizon optimal control problems (1986)
    Springer
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938602
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  • 20
    Electronic Resource
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    Closed-form recursive formula for an optimal tracker with terminal constraints (1986)
    Springer
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939827
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  • 21
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939830
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  • 22
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    Finding candidate singular optimal controls: A state of the art survey (1989)
    Springer
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940004
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  • 23
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    A new technique for linear static state estimation based on weighted least absolute value approximations (1989)
    Springer
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940848
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  • 24
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    Linear quadratic optimal control for discrete descriptor systems (1989)
    Springer
    Journal of optimization theory and applications 61 (1989), S. 221-245 
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    ISSN: 1573-2878
    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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    URL: http://dx.doi.org/10.1007/BF00962798
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  • 25
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    Minimal trajectories of nonconvex differential inclusions (1989)
    Springer
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00941824
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  • 26
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    Sufficient optimality conditions for nonconvex control problems with state constraints (1989)
    Springer
    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
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1007/BF00941059
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  • 27
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    A solution method for regular optimal control problems with state constraints (1989)
    Springer
    Journal of optimization theory and applications 62 (1989), S. 489-513 
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    ISSN: 1573-2878
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939818
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  • 28
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    Nonlinear optimal control problems with continuous state inequality constraints (1989)
    Springer
    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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  • 29
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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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  • 30
    Electronic Resource
    Electronic Resource
    A new sufficient condition for most rapid approach paths (1987)
    Springer
    Journal of optimization theory and applications 54 (1987), S. 403-411 
    Details
    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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  • 31
    Electronic Resource
    Electronic Resource
    Local convergence of an algorithm for solving optimal control problems (1985)
    Springer
    Journal of optimization theory and applications 46 (1985), S. 265-293 
    Details
    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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