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  • Articles  (39)
  • Optimal control  (28)
  • stability
  • Springer  (39)
  • 1980-1984  (39)
  • Mathematics  (39)
  • Process Engineering, Biotechnology, Nutrition Technology
  • 1
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    A stability investigation for an incompressible simple fluid with fading memory (1980)
    Springer
    Archive for rational mechanics and analysis 72 (1980), S. 203-218 
    Details
    ISSN: 1432-0673
    Keywords: simple fluid ; viscoelastic ; fading memory ; stability ; Liapunov function ; dynamical system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The nonlinear equations of motion for an incompressible simple fluid, occupying a fixed bounded container, are formulated on the basis of the “finitelinear” viscoelasticity theory for materials with fading memory; this formal boundary-initial value problem is then viewed as a nonlinear abstract evolution equation on a certain Hilbert space. It is shown that a linearized version of this evolution equation is associated with a linear dynamical system on this Hilbert space, and several results for stability and asymptotic behavior for this linearized problem are proved through the use of Liapunov stability methods. On the assumption that the original nonlinear evolution equation also is associated with some dynamical system on the same space, it is shown that the rest condition of the fluid is stable and all motions are bounded. The Liapunov function employed for this purpose can be interpreted as a mechanical energy function for the fluid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00281589
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  • 2
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    Analysis of a sterile insect release model with predation (1982)
    Springer
    Journal of mathematical biology 16 (1982), S. 33-48 
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    ISSN: 1432-1416
    Keywords: Sterile insect release ; Predation ; Stability ; Limit cycles ; Optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model for the sterile insect release method of pest control in which the target species is under predatory or parasitic regulation is analyzed. The equations are nondimensionalized and the rescaled parameters are interpreted. There are four types of equilibria, whose existence and stability depend on which of ten regions of parameter space contain the rescaled parameters, and in turn give minimal release rates to achieve eradication of the pest. In at least one region, Hopf bifurcation theory shows the existence of limit cycles, but they are found to be unstable. In addition, the optimal release rate to minimize a total cost functional for pest control by the sterile release method is studied. Both approaches show that when predation accounts for a large fraction of the natural deaths, the necessary release rate and total cost are higher than for weak predation. If the predators are removed without being replaced by any other source of mortality, the cost rises in all cases but rises much more dramatically for cases with strong predation. A definite danger of the sterile release method when some predatory control exists is that the predators are frequently driven extinct before the prey, so that the target species could explode to much higher levels and be more difficult to eradicate again after the sterile release is terminated.
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    URL: http://dx.doi.org/10.1007/BF00275159
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  • 3
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    Existence and stability of equilibria in age-structured population dynamics (1984)
    Springer
    Journal of mathematical biology 20 (1984), S. 259-276 
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    ISSN: 1432-1416
    Keywords: Age-structured population dynamics ; equilibria ; stability ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. The local existence and uniqueness of a branch of positive equilibria which bifurcates from the trivial (identically zero) solution at the critical value n=1 are proved by implicit function techniques under very mild smoothness conditions on the death and fertility rates as functional of age and population density. This first requires the development of a suitable linear theory. The lowest order terms in the Liapunov-Schmidt expansions are also calculated. This local analysis supplements earlier global bifurcation results of the author. The stability of both the trivial and the positive branch equilibria is studied by means of the principle of linearized stability. It is shown that in general the trivial solution losses stability as n increases through one while the stability of the branch solution is stable if and only if the bifurcation is supercritical. Thus the McKendrick equations exhibit, in the latter case, a standard exchange of stability with regard to equilibrium states as they depend on the inherent net reproductive rate. The derived lower order terms in the Liapunov-Schmidt expansions yield formulas which explicitly relate the direction of bifurcation to properties of the age-specific death and fertility rates as functionals of population density. Analytical and numerical results for some examples are given which illustrate these results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275988
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  • 4
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    Predator-prey relationships: Indiscriminate predation (1984)
    Springer
    Journal of mathematical biology 21 (1984), S. 25-34 
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    ISSN: 1432-1416
    Keywords: Predator-prey ; density dependence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Gurtin and Levine model5 is studied in this paper under the assumption that the fecundity of prey depends on age as well as on the total population sizes of prey and predators. The purpose of this study is to see the effect of this density dependence on the stability criteria for the equilibria of the model equations. It is shown that there are cases when, due to density dependence, the model which is originally neutrally stable becomes stable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275220
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  • 5
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    Some remarks on the existence of optimal controls for quasilinear systems (1981)
    Springer
    Journal of optimization theory and applications 33 (1981), S. 393-399 
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    ISSN: 1573-2878
    Keywords: Optimal control ; nonlinear systems ; existence theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let a quasilinear control system having the state space $$\bar X \subseteq R^n $$ be governed by the vector differential equation $$\dot x = G(u(t))x,$$ wherex(0) =x 0 andU is the family of all bounded measurable functions from [0,T] intoU, a compact and convex subset ofR m.LetG:U ⇑R be a bounded measurable nonlinear function, such thatG(U) is compact and convex.G −1 can be convex onG(U) or concave. The main results of the paper establish the existence of a controlu ∈U which minimizes the cost functional $$I(u) = \int_0^T {L(u(t))x(t)dt,} $$ whereL(·) is convex. A practical example of application for chemical reactions is worked out in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935251
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  • 6
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    Sufficient conditions for the optimal control of a class systems with continuous lags (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 153-154 
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    ISSN: 1573-2878
    Keywords: Optimal control ; maximum principle ; sufficient conditions ; integro-differential equations ; path constraints ; economic applications
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Notational errors in Theorem 5.2 of Ref. 1 are corrected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934332
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  • 7
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    Method of reduction in convex programming (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 349-378 
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    ISSN: 1573-2878
    Keywords: Convexity ; subdifferentials ; cones of directions of constancy ; equality set of constraints ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present an algorithm which solves a convex program with faithfully convex (not necessarily differentiable) constraints. While finding a feasible starting point, the algorithm reduces the program to an equivalent program for which Slater's condition is satisfied. Included are algorithms for calculating various objects which have recently appeared in the literature. Stability of the algorithm is discussed.
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    URL: http://dx.doi.org/10.1007/BF00933505
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  • 8
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    On the optimal control problem of a single-server queueing system (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 317-325 
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    ISSN: 1573-2878
    Keywords: Optimal control ; queueing theory ; phase type distributions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a single-server queueing system (with a finite waiting room) with phase type arrivals and exponential service times, an optimal control for the service rate is derived. This generalizes the result of Scott and Jefferson for theM/M/1/1 queueing model.
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    URL: http://dx.doi.org/10.1007/BF00935227
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  • 9
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    Near-optimum design of nonstationary linear systems with state and control delays (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 73-88 
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    ISSN: 1573-2878
    Keywords: Optimal control ; suboptimal control ; time-delay systems ; linear systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A computationally efficient method based on a sensitivity approach is developed to obtain suboptimal control for nonstationary linear systems with multiple state and control delays and with quadratic cost. The proposed suboptimal control includes some truncated series whose terms are calculated in a recursive manner from nondelay system optimization.
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    URL: http://dx.doi.org/10.1007/BF00934590
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  • 10
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    Stability of nondominated solutions in multicriteria decision-making (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 229-253 
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    ISSN: 1573-2878
    Keywords: Point-to-set maps ; domination structures ; parameterized decision-making problems ; solution maps ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Decision-making problems with multiple noncommensurable objectives are specified by two factors, i.e., the set of all feasible solutions and the domination structure. The solutions are characterized as nondominated points. Hence, in these problems, there may exist two parameter vectors, according to which the above two factors change. The stability of the solution set for perturbations of these parameters is investigated in this paper. The analysis is guided by using the concept of continuity of the solution map defined on the two parameter spaces.
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    URL: http://dx.doi.org/10.1007/BF00934497
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  • 11
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    Suboptimal control of systems with multiple delays (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 621-633 
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    ISSN: 1573-2878
    Keywords: Optimal control ; time-delay systems ; linear systems ; multiple-delay systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The application of Pontryagin's maximum principle to the optimization of linear systems with time delays results in a system of coupled two-point boundary-value problems involving both delay and advance terms. The exact solution of this system of TPBV problems is extremely difficult, if not impossible. In this paper, a fast-converging iterative approach is developed for obtaining the suboptimal control for nonstationary linear systems with multiple state and control delays and with quadratic cost. At each step of the proposed method, a linear nondelay system with an extra perturbing input must be optimized. The procedure can be extended for the optimization of nonlinear systems with multiple time-varying delays, provided that some of the nonlinearities satisfy the Lipschitz condition.
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    URL: http://dx.doi.org/10.1007/BF01686725
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  • 12
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    Solution of nonlinear optimal control problems in Hilbert spaces by means of linear programming techniques (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 643-661 
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    ISSN: 1573-2878
    Keywords: Optimal control ; measures ; Hilbert spaces ; linear programming ; approximation techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Optimal control problems in Hilbert spaces are considered in a measure-theoretical framework. Instead of minimizing a functional defined on a class of admissible trajectory-control pairs, we minimize one defined on a set of measures; this set is defined by the boundary conditions and the differential equation of the problem. The new problem is an infinite-dimensionallinear programming problem; it is shown that it is possible to approximate its solution by that of a finite-dimensional linear program of sufficiently high dimensions, while this solution itself can be approximated by a trajectory-control pair. This pair may not be strictly admissible; if the dimensionality of the finite-dimensional linear program and the accuracy of the computations are high enough, the conditions of admissibility can be said to be satisfied up to any given accuracy. The value given by this pair to the functional measuring the performance criterion can be about equal to theglobal infimum associated with the classical problem, or it may be less than this number. It appears that this method may become a useful technique for the computation of optimal controls, provided the approximations involved are acceptable.
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    URL: http://dx.doi.org/10.1007/BF01686727
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  • 13
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    Junction phenomena for optimal control with state-variable inequality constraints of third order (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 85-99 
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    ISSN: 1573-2878
    Keywords: Optimal control ; junction conditions ; calculus of variations ; inequality constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is known that extremal arcs governed by inequality constraints of third order (constraint relations that must be differentiated three times to generate a control equation) cannot join an unconstrained arc, except in special cases. But a control problem is exhibited, for which every extremal includes a constrained arc of third order. The constrained arc joins the end of an infinite sequence of consecutive unconstrained arcs of finite total duration. Evidence (but not proof) is given that this phenomenon is typical, rather than exceptional. An analogous phenomenon is well known for optimal control problems with singular arcs of second order.
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    URL: http://dx.doi.org/10.1007/BF00934790
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  • 14
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    Existence and global asymptotic stability of optimal trajectories for a class of infinite-horizon, nonconvex systems (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 515-533 
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    ISSN: 1573-2878
    Keywords: Optimal control ; economic systems ; stability ; existence theory ; turnpike property
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Sufficient conditions for the existence of optimal trajectories and for the global asymptotic stability of these trajectories are given for a class of nonconvex and nonautonomous systems controlled over an infinite-time horizon. The concept ofG-supported trajectory is introduced. It is shown that, under some assumptions, aG-supported trajectory is overtaking and is globally asymptotically stable. The concept of overtaking trajectory has been previously defined as a notion of optimality on an infinite-time domain. For autonomous systems, under weaker conditions, one guarantees the existence of weakly overtaking trajectories. Finally, it is shown howG-supported trajectories can be obtained, and an application to the study of a pre-predator ecosystem optimally harvested is sketched.
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    URL: http://dx.doi.org/10.1007/BF00934475
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  • 15
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    On optimal control problems with state constraints (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 75-80 
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    ISSN: 1573-2878
    Keywords: Optimal control ; state constraints ; multipliers ; perturbation theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with necessary conditions for a general optimal control problem developed by Russak and Tan. It is shown that, in most cases, a further relation between the multipliers holds. This result is of interest in particular for the investigation of perturbations of the state constraint.
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    URL: http://dx.doi.org/10.1007/BF00934843
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  • 16
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    A property of an autonomous minimax optimal control problem (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 81-87 
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    ISSN: 1573-2878
    Keywords: Optimal control ; minimax problems ; maximum principle ; Hamiltonian function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A control system $$\dot x = f\left( {x,u} \right)$$ ,u) with cost functional $$\mathop {ess \sup }\limits_{T0 \leqslant t \leqslant T1} G\left( {x\left( t \right),u\left( t \right)} \right)$$ is considered. For an optimal pair $$\left( {\bar x\left( \cdot \right),\bar u\left( \cdot \right)} \right)$$ ,ū(·)), there is a maximum principle of the form $$\eta \left( t \right)f\left( {\bar x\left( t \right),\bar u\left( t \right)} \right) = \mathop {\max }\limits_{u \in \Omega \left( t \right)} \eta \left( t \right)f\left( {\bar x\left( t \right),u} \right).$$ By means of this fact, it is shown that $$\eta \left( t \right)f\left( {\bar x\left( t \right),\bar u\left( t \right)} \right)$$ is equal to a constant almost everywhere.
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    URL: http://dx.doi.org/10.1007/BF00934844
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  • 17
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    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 1 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 211-246 
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    ISSN: 1573-2878
    Keywords: Optimal control ; control constraints ; terminal equality constraints ; exact penalty function ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The presence of control constraints, because they are nondifferentiable in the space of control functions, makes it difficult to cope with terminal equality constraints in optimal control problems. Gradient-projection algorithms, for example, cannot be employed easily. These difficulties are overcome in this paper by employing an exact penalty function to handle the cost and terminal equality constraints and using the control constraints to define the space of permissible search directions in the search-direction subalgorithm. The search-direction subalgorithm is, therefore, more complex than the usual linear program employed in feasible-directions algorithms. The subalgorithm approximately solves a convex optimal control problem to determine the search direction; in the implementable version of the algorithm, the accuracy of the approximation is automatically increased to ensure convergence.
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    URL: http://dx.doi.org/10.1007/BF00934725
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  • 18
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    Sufficient conditions for asymptotic optimal control (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 307-325 
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    ISSN: 1573-2878
    Keywords: Optimal control ; asymptotic optimal control ; calculus of variations ; Lagrange problems ; global minima ; absolute minima ; necessary conditions ; sufficient conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a selected family of Lagrange-type control problems involving a nonnegative integral costJ T (y,u) over the interval [0,T], 0〈T〈∞, with system conditions consisting of differential inequalities and/or equalities, the following material is treated: (i) a resumé of relevant necessary conditions and sufficient conditions for a pair (y T ,u T ) to minimizeJ T (y,u); (ii) conditions sufficient for the convergence asT→∞ of minimizing pairs (y T ,u T ) over [0,T] to a limit pair (y ∞,u ∞) over the infinite-time interval [0, ∞); (iii) conditions sufficient for (y ∞,u ∞) to minimize the costJ ∞(y,u) over [0, ∞); and (iv) conditions sufficient for the optimal cost per unit timeJ T (y T ,u T )/T to have a limit asT→∞.
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    URL: http://dx.doi.org/10.1007/BF00934555
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  • 19
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    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 2 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 345-364 
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    ISSN: 1573-2878
    Keywords: Optimal control ; control constraints ; terminal equality constraints ; exact penalty functions ; convergence ; relaxed control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Part 1 of this paper, implementable and conceptual versions of an algorithm for optimal control problems with control constraints and terminal equality constraints were presented. It was shown that anyL ∞ accumulation points of control sequences generated by the algorithms satisfy necessary conditions of optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithms always have accumulation points in the sense of control measure, and these accumulation points satisfy optimality conditions for the corresponding relaxed control problem.
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    URL: http://dx.doi.org/10.1007/BF00934557
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  • 20
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    On the order of singular optimal control problems (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 479-489 
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    ISSN: 1573-2878
    Keywords: Optimal control ; singular control ; junction conditions ; singular control order
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In singular optimal control problems, the functional form of the optimal control function is usually determined by solving the algebraic equation which results by successively differentiating the switching function until the control appears explicitly. This process defines the order of the singular problem. Order-related results are developed for singular linear-quadratic problems and for a bilinear example which gives new insights into the relationship between singular problem order and singular are order.
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    URL: http://dx.doi.org/10.1007/BF00934035
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  • 21
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    On the general inverse problem of optimal control theory (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 491-497 
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    ISSN: 1573-2878
    Keywords: Optimal control ; inverse problems ; dynamic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The general inverse problem of optimal control is considered from a dynamic programming point of view. Necessary and sufficient conditions are developed which two integral criteria must satisfy if they are to yield the same optimal feedback law, the dynamics being fixed. Specializing to the linear-quadratic case, it is shown how the general results given here recapture previously obtained results for quadratic criteria with linear dynamics.
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    URL: http://dx.doi.org/10.1007/BF00934036
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  • 22
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    Stability of compromise solution in multicriteria decision-making problems (1983)
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    Journal of optimization theory and applications 40 (1983), S. 77-83 
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    ISSN: 1573-2878
    Keywords: Parameterized decision-making problems ; utopia point ; compromise solutions ; Hausdorff distance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Stability is a desirable attribute of the nondominated solution in the decision-making problem with multiple noncommensurable objectives. It is assumed that the decision space is given by a system of inequalitiesG(x)≤b, b ∈ R N . In this paper, sufficient conditions are determined for a compromise solution to be stable with respect to the changes ofb.
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    URL: http://dx.doi.org/10.1007/BF00934632
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  • 23
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    Realistic feedback control of two interconnected turbogenerators (1984)
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    Journal of optimization theory and applications 42 (1984), S. 103-141 
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    ISSN: 1573-2878
    Keywords: Optimal control ; realistic feedback control ; interconnected turbogenerators ; torque and voltage control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the optimal control of a system with two identical interconnected turbogenerators, which are connected to an infinite bus, is considered. The alternators are controlled through a linear feedback of the state variables. The feedback parameters are obtained by solving a nonlinear, two-point boundary-value problem. The values obtained for these parameters depend on the strength and duration of the disturbance, since the model is nonlinear, contrary to the usual feedback control of a linear model. In contrast to the model used in Ref. 1, the model used here includes the transfer function of the governors, the turbines, and the voltage regulators.
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    URL: http://dx.doi.org/10.1007/BF00934135
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    Convergence of a strong variational algorithm for relaxed controls involving a class of hyperbolic systems (1984)
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    Journal of optimization theory and applications 42 (1984), S. 467-485 
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    ISSN: 1573-2878
    Keywords: Optimal control ; hyperbolic partial differential equations ; Darboux boundary conditions ; strong variational algorithm ; convergence ; relaxed control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of optimal control problems involving linear hyperbolic partial differential equations with Darboux boundary conditions. A strong variational algorithm has been obtained for solving this class of optimal control problems in a previous paper by the third and the first authors. It was also shown that anyL ∞ accumulation points of control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown in this paper that the control sequences generated by the algorithm always have accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed control problems.
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    URL: http://dx.doi.org/10.1007/BF00935327
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  • 25
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    Necessary and sufficient conditions for optimal control of quasilinear partial differential systems (1984)
    Springer
    Journal of optimization theory and applications 43 (1984), S. 89-101 
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    ISSN: 1573-2878
    Keywords: Optimal control ; distributed-parameter systems ; control of partial differential equations ; sufficiency conditions ; Green's formula
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract First-order necessary and sufficient conditions are obtained for the following quasilinear distributed-parameter optimal control problem: $$max\left\{ {J(u) = \int_\Omega {F(x,u,t) d\omega + } \int_{\partial \Omega } {G(x,t) \cdot d\sigma } } \right\},$$ subject to the partial differential equation $$A(t)x = f(x,u,t),$$ wheret,u,G are vectors andx,F are scalars. Use is made of then-dimensional Green's theorem and the adjoint problem of the equation. The second integral in the objective function is a generalized surface integral. Use of then-dimensional Green's theorem allows simple generalization of single-parameter methods. Sufficiency is proved under a concavity assumption for the maximized Hamiltonian $$H^\circ (x,\lambda ,t) = \max \{ H(x,u,\lambda ,t):u\varepsilon K\} $$ .
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    URL: http://dx.doi.org/10.1007/BF00934748
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  • 26
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    Optimal control of a rotary crane (1981)
    Springer
    Journal of optimization theory and applications 35 (1981), S. 535-557 
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    ISSN: 1573-2878
    Keywords: Optimal control ; rotary crane ; nonlinear systems ; computational algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the optimal control of a rotary crane, which makes two kinds of motion (rotation and hoisting) at the same time. The optimal control which transfers a load to a desired place as fast as possible and minimizes the swing of the load during the transfer, as well as the swing at the end of transfer, is calculated on the basis of a dynamic model. A new computational technique is employed for computing the optimal control, and several numerical results are presented.
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    URL: http://dx.doi.org/10.1007/BF00934931
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    Stochastic scheduling problems I — General strategies (1984)
    Springer
    Mathematical methods of operations research 28 (1984), S. 193-260 
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    ISSN: 1432-5217
    Keywords: Analytic behaviour of strategies ; continuous strategies ; ES strategies ; MES strategies ; machine idleness ; monotonicity behaviour ; optimal strategies ; preselectivity ; regular measure of performance ; scheduling problems ; stability ; stochastic dynamic optimization ; stochastically ordered distributions ; stochastic scheduling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The paper contains an introduction to recent developments in the theory of non-preemptive stochastic scheduling problems. The topics covered are: arbitrary joint distributions of activity durations, arbitrary regular measures of performance and arbitrary precedence and resource constraints. The possible instability of the problem is demonstrated and hints are given on stable classes of strategies available, including the combinatorial vs. analytical characterization of such classes. Given this background, the main emphasis of the paper is on the monotonicity behaviour of the model and on the existence of optimal strategies. Existing results are presented and generalized, in particular w.r.t. the cases of lower semicontinuous performance measures or joint duration distributions having a Lebesgue density.
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    URL: http://dx.doi.org/10.1007/BF01919323
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    Optimal control of distributed nuclear reactors using functional analysis (1981)
    Springer
    Journal of optimization theory and applications 34 (1981), S. 445-458 
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    ISSN: 1573-2878
    Keywords: Optimal control ; distributed parameter systems ; nuclear reactors ; functional analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The minimum norm formalism of functional analysis is applied to the problem of minimizing a quadratic cost functional that penalizes the control effort and the deviations of the neutron flux distribution throughout the reactor core. The conditions for optimality are derived for a general, linearized, reactor model with a finite number of control rods. These conditions take the form of a coupled and finite set of Fredholm's integral equations of the second kind with nondegenerate kernels. An example is presented in which the homogeneous slab reactor model is considered. A contraction mapping algorithm is proposed to compute the optimal control.
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    URL: http://dx.doi.org/10.1007/BF00934682
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    Additional necessary conditions for optimal control with state-variable inequality constraints (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 241-250 
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    ISSN: 1573-2878
    Keywords: Optimal control ; state constraints ; necessary conditions for optimality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown that, when the set of necessary conditions for an optimal control problem with state-variable inequality constraints given by Bryson, Denham, and Dreyfus is appropriately augmented, it is equivalent to the (different) set of conditions given by Jacobson, Lele, and Speyer. Relationships among the various multipliers are given.
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    URL: http://dx.doi.org/10.1007/BF00934086
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    Conflict dissolution by reframing game payoffs using linear perturbations (1983)
    Springer
    Journal of optimization theory and applications 39 (1983), S. 187-214 
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    ISSN: 1573-2878
    Keywords: Self-interest maximization ; self-interest stable solutions ; self-interest cooperative games ; self-interest noncooperative games ; monotonic games ; decomposition theory ; reframing game payoffs ; full cooperation ; targeted solutions ; Pareto optimality ; collective group interest ; stability ; structural departure ; incentives for adopting a new game ; habitual domain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Human beings have a prevailing drive to achieve their self-interest goals or equilibrium states, which may subsume their social interests. An ideal working environment or cooperative game situation would be one in which each participant or player maximizes his/her own interest while maximizing his/her contribution to the collective group interest. This paper addresses the feasibility, methods, and bounds for reframing a generaln-person game into an ideal game in which full cooperation or a targeted solution can be induced and maintained by the players' self-interest maximization. Criteria for good reframing are introduced. Monotonic games, self-interest cooperative and noncooperative games, and a decomposition theory of general games are also introduced to facilitate the study. It is shown that everyn-person game can be written as the sum of a self-interest cooperative game and a self-interest noncooperative game. Everyn-person game can be reframed so that full cooperation can be achieved by the players' self-interest maximization. Everyn-person game can be reframed so that a targeted solution can be obtained and maintained through the players' self-interest maximization.
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    URL: http://dx.doi.org/10.1007/BF00934528
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    Second-order necessary conditions in optimal control: Accessory-problem results without normality conditions (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 75-106 
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    ISSN: 1573-2878
    Keywords: Optimal control ; second-order necessary conditions ; accessory problem ; control constraints ; normality condition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An optimal control problem, which includes restrictions on the controls and equality/inequality constraints on the terminal states, is formulated. Second-order necessary conditions of the accessory-problem type are obtained in the absence of normality conditions. It is shown that the necessary conditions generalize and simplify prior results due to Hestenes (Ref. 5) and Warga (Refs. 6 and 7).
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    URL: http://dx.doi.org/10.1007/BF00934437
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    Optimum load scheduling of nuclear-hydro-thermal power systems (1981)
    Springer
    Journal of optimization theory and applications 35 (1981), S. 261-275 
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    ISSN: 1573-2878
    Keywords: Optimal control ; load scheduling ; nuclear-hydro-thermal power systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper considers the problem of short-term optimal operation of nuclear-hydro-thermal electric power systems. The solution is obtained by use of a functional analytic optimization technique that employs the minimum norm formulation. A power system with an arbitrary number of generating stations is considered. The limited flexibility exhibited by the thermal nuclear reactors, when operating in a load-following mode, is accounted for by means of a model of the xenon concentration in their cores. The nonlinear effects induced by trapezoidal water reservoirs and the time delay of the water flow between upstream and downstream hydroplants is taken into consideration as well. A two-level iterative scheme of the feasible type is proposed for implementing the optimal solution.
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    URL: http://dx.doi.org/10.1007/BF00934580
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    Decentralized control with overlapping information sets (1981)
    Springer
    Journal of optimization theory and applications 34 (1981), S. 279-310 
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    ISSN: 1573-2878
    Keywords: Decentralized control ; overlapping decompositions ; suboptimality ; stability ; interconnected power systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A decentralized control scheme is proposed for linear systems composed of overlapping subsystems. By expanding the state space of the system, a higher-dimensional space is formed where the subsystems appear as disjoint. In the expanded space, standard optimization techniques can be used to formulate a suboptimal decentralized control law for the overall system. A suitable contraction of the obtained control law, which is compatible with the information constraints imposed by the overlapping subsystems, can be implemented in the original system. The application of the proposed decentralized control scheme is illustrated using a 19th order model for load-frequency control of a two-area interconnected power system.
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    URL: http://dx.doi.org/10.1007/BF00935477
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    Contour of complete nonuniqueness as a method of structural optimization with stability constraints (1981)
    Springer
    Journal of optimization theory and applications 35 (1981), S. 23-30 
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    ISSN: 1573-2878
    Keywords: Contour of complete nonuniqueness ; trusses ; stability ; structural optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper develops the concept of a contour of complete nonuniqueness and shows its application to the optimal design (optimal layout) of simple trusses transmitting a concentrated force to a presscribed, arbitrary foundation contour. As an example, a symmetric two-bar truss with compressed bars is considered, and the constraints refer to various kinds of elastic instability of the system.
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    URL: http://dx.doi.org/10.1007/BF00934701
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    Duality for nonlinear multiple-criteria optimization problems (1981)
    Springer
    Journal of optimization theory and applications 35 (1981), S. 367-401 
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    ISSN: 1573-2878
    Keywords: Multiple-criteria decision making ; vector-valued duality ; saddle-point duality ; Kuhn-Tucker conditions ; Pareto optimality ; stability ; efficient points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we develop a duality theory for nonlinear multiple-criteria optimization problems. The theory associates to efficient points a matrix, rather than a vector, of dual variables. We introduce a saddle-point dual problem, study stability concepts and Kuhn-Tucker conditions, and provide an economic interpretation of the dual matrix. The results are compared to the classical approach of deriving duality, by applying nonlinear programming duality theory to a problem obtained by conveniently weighting the criteria. Possible directions for future research are discussed.
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    URL: http://dx.doi.org/10.1007/BF00934908
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    Optimal control of a large turboalternator (1981)
    Springer
    Journal of optimization theory and applications 34 (1981), S. 83-97 
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    ISSN: 1573-2878
    Keywords: Optimal control ; large turboalternators ; torque control ; voltage control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The optimal torque and voltage control for a large turbogenerator is found by using the minimum norm formulation. It should be noted that the model used is highly nonlinear. Numerical results are presented.
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    URL: http://dx.doi.org/10.1007/BF00933358
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    Dynamic programming using singular perturbations (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 221-230 
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    ISSN: 1573-2878
    Keywords: Optimal control ; dynamic programming ; singular perturbations ; system order reduction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The singular perturbation method is used in dynamic programming to reduce the order and the computational requirements of linear systems composed of slow and fast modes. After the fast modes are separated, a near-optimum solution is computed at two different iteration rates determined by the slow and fast subsystem dynamics. The result is a reduction in the order of the computational requirement of the given system to that of the slow subsystem.
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    URL: http://dx.doi.org/10.1007/BF00934084
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    Optimal control of two interconnected turbogenerators (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 255-291 
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    ISSN: 1573-2878
    Keywords: Optimal control ; two interconnected turbogenerators ; torque control ; voltage control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the optimal control of a system with two identical interconnected turbogenerators, which are connected to an infinite bus, is considered. Control of the generators is effected through control of field voltages and turbine torques. The alternators are controlled through a linear feedback of the state variables. The feedback parameters are obtained by solving a nonlinear, two-point boundary-value problem. The values obtained for these parameters depend on the strength and duration of the disturbance, since the model is nonlinear, in contrast to the usual feedback control of a linear model. The numerical values used are indicated in the Appendix.
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    URL: http://dx.doi.org/10.1007/BF00933940
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    Feasible direction method for large-scale nonconvex programs: Decomposition approach (1981)
    Springer
    Journal of optimization theory and applications 35 (1981), S. 231-249 
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    ISSN: 1573-2878
    Keywords: Optimal control ; nonconvex programming ; constrained optimization ; feasible direction methods ; dual decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we propose a feasible-direction method for large-scale nonconvex programs, where the gradient projection on a linear subspace defined by the active constraints of the original problem is determined by dual decomposition. Results are extended for dynamical problems which include distributed delays and constraints both in state and control variables. The approach is compared with other feasible-direction approaches, and the method is applied to a power generation problem. Some computational results are included.
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    URL: http://dx.doi.org/10.1007/BF00934578
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