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  • Articles  (63)
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  • optimal control  (63)
  • 2010-2014
  • 2000-2004  (20)
  • 1985-1989  (22)
  • 1980-1984  (21)
  • Mathematics  (63)
  • 1
    Electronic Resource
    Electronic Resource
    Optimal Control of One-Dimensional Partial Differential Algebraic Equations with Applications (2000)
    Springer
    Annals of operations research 98 (2000), S. 45-64 
    Details
    ISSN: 1572-9338
    Keywords: optimal control ; partial differential equations ; numerical methods ; transdermal systems ; acetylene reactors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We present an approach to compute optimal control functions in dynamic models based on one-dimensional partial differential algebraic equations (PDAE). By using the method of lines, the PDAE is transformed into a large system of usually stiff ordinary differential algebraic equations and integrated by standard methods. The resulting nonlinear programming problem is solved by the sequential quadratic programming code NLPQL. Optimal control functions are approximated by piecewise constant, piecewise linear or bang-bang functions. Three different types of cost functions can be formulated. The underlying model structure is quite flexible. We allow break points for model changes, disjoint integration areas with respect to spatial variable, arbitrary boundary and transition conditions, coupled ordinary and algebraic differential equations, algebraic equations in time and space variables, and dynamic constraints for control and state variables. The PDAE is discretized by difference formulae, polynomial approximations with arbitrary degrees, and by special update formulae in case of hyperbolic equations. Two application problems are outlined in detail. We present a model for optimal control of transdermal diffusion of drugs, where the diffusion speed is controlled by an electric field, and a model for the optimal control of the input feed of an acetylene reactor given in form of a distributed parameter system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019231718807
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  • 2
    Electronic Resource
    Electronic Resource
    The Optimal Control of a Train (2000)
    Springer
    Annals of operations research 98 (2000), S. 65-87 
    Details
    ISSN: 1572-9338
    Keywords: train control ; optimal control ; discrete control ; optimal switching times
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider the problem of determining an optimal driving strategy in a train control problem with a generalised equation of motion. We assume that the journey must be completed within a given time and seek a strategy that minimises fuel consumption. On the one hand we consider the case where continuous control can be used and on the other hand we consider the case where only discrete control is available. We pay particular attention to a unified development of the two cases. For the continuous control problem we use the Pontryagin principle to find necessary conditions on an optimal strategy and show that these conditions yield key equations that determine the optimal switching points. In the discrete control problem, which is the typical situation with diesel-electric locomotives, we show that for each fixed control sequence the cost of fuel can be minimised by finding the optimal switching times. The corresponding strategies are called strategies of optimal type and in this case we use the Kuhn–Tucker equations to find key equations that determine the optimal switching times. We note that the strategies of optimal type can be used to approximate as closely as we please the optimal strategy obtained using continuous control and we present two new derivations of the key equations. We illustrate our general remarks by reference to a typical train control problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019235819716
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  • 3
    Electronic Resource
    Electronic Resource
    Average Cost Optimality for an Unreliable Two-Machine Flowshop with Limited Internal Buffer (2000)
    Springer
    Annals of operations research 98 (2000), S. 333-351 
    Details
    ISSN: 1572-9338
    Keywords: production planning ; stochastic dynamic programming ; optimal control ; long-run average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019272811055
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  • 4
    Electronic Resource
    Electronic Resource
    On Quantitative Stability in Optimization and Optimal Control (2000)
    Springer
    Set-valued analysis 8 (2000), S. 31-50 
    Details
    ISSN: 1572-932X
    Keywords: stability in optimization ; generalized equations ; Lipschitz continuity ; mathematical programming ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study two continuity concepts for set-valued maps that play central roles in quantitative stability analysis of optimization problems: Aubin continuity and Lipschitzian localization. We show that various inverse function theorems involving these concepts can be deduced from a single general result on existence of solutions to an inclusion in metric spaces. As applications, we analyze the stability with respect to canonical perturbations of a mathematical program in a Hilbert space and an optimal control problem with inequality control constraints. For stationary points of these problems, Aubin continuity and Lipschitzian localization coincide; moreover, both properties are equivalent to surjectivity of the map of the gradients of the active constraints combined with a strong second-order sufficient optimality condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008714222851
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  • 5
    Electronic Resource
    Electronic Resource
    Numerical Schemes for Discontinuous Value Functions of Optimal Control (2000)
    Springer
    Set-valued analysis 8 (2000), S. 111-126 
    Details
    ISSN: 1572-932X
    Keywords: viability ; optimal control ; value function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we explain that various (possibly discontinuous) value functions for optimal control problem under state-constraints can be approached by a sequence of value functions for suitable discretized systems. The key-point of this approach is the characterization of epigraphs of the value functions as suitable viability kernels. We provide new results for estimation of the convergence rate of numerical schemes and discuss conditions for the convergence of discrete optimal controls to the optimal control for the initial problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008774508738
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  • 6
    Electronic Resource
    Electronic Resource
    Optimal dynamic routing in Flexible Manufacturing Systems with limited buffers (1988)
    Springer
    Annals of operations research 15 (1988), S. 289-311 
    Details
    ISSN: 1572-9338
    Keywords: Flexible manufacturing system ; dynamic routing ; material handling ; robotics ; semi-Markovian decision process ; optimal control ; stochastic optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract An optimal routing policy is obtained for Flexible Manufacturing Systems (FMSs) with limited buffers at the work stations. This policy is used to effectively drive a robotic material handling system. The routing decisions are made by a supervising computer on a real-time basis in order to avoid any work station running out of inputs and to control the blocking of the material handling system. Using our model, general material handling times can be assumed. The optimal policy and several key performance measures are computed, following the problem formulation as a continuous-time, semi-Markovian decision process. Fast convergence and computational stability are ensured by the ergodic solution algorithm augmented to solve the functional equations of the renewal process. The solution algorithm was implemented, tested on an extensive range of problems regarding the structure and the performance of the optimal policy. Complex environments involving diverse processing times, as well as very limited buffer storage, were examined. The interaction between the allocation of buffer spaces to work stations, the structural properties of the optimal monotone (threshold-type) policy and the system performance are also investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186800
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  • 7
    Electronic Resource
    Electronic Resource
    Approximate Optimal Control and Stability of Nonlinear Finite- and Infinite-Dimensional Systems (2000)
    Springer
    Annals of operations research 98 (2000), S. 19-44 
    Details
    ISSN: 1572-9338
    Keywords: optimal control ; nonlinear systems ; parabolic systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider first nonlinear systems of the form x=A(x)x+B(x)u together with a standard quadratic cost functional and replace the system by a sequence of time-varying approximations for which the optimal control problem can be solved explicitly. We then show that the sequence converges. Although it may not converge to a global optimal control of the nonlinear system, we also consider a similar approximation sequence for the equation given by the necessary conditions of the maximum principle and we shall see that the first method gives solutions very close to the optimal solution in many cases. We shall also extend the results to parabolic PDEs which can be written in the above form on some Hilbert space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019279617898
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  • 8
    Electronic Resource
    Electronic Resource
    Maximum Principle for a Control Problem Governed by an Evolution Equation (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 263-276 
    Details
    ISSN: 1573-2878
    Keywords: optimal control ; distributed-parameter systems ; Pontryagin maximum principle ; Ekeland variational principle ; unbounded controls
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove the maximum principle for an optimal control problem governed by the system $$y'(t) + A(t)y(t) = f(t,y(t),u(t)),{\text{ }}u(t) \in U(t), $$ with state constraint $$(y(0),y(T)) \in C \subset H \times H $$ , under three different hypotheses: (H1) C is a convex set with nonempty interior; (H2) $$C = \{ y_0 \} \times C_{0,} {\text{ with }}C_0 $$ a convex set with nonempty interior in H and the evolution system satisfying compactness hypotheses; (H3) the periodic case $$y(0) = y(T)$$ , with the evolution system satisfying compactness hypotheses. We do not assume the controls to be bounded. We give some examples for distributed control problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004654800011
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  • 9
    Electronic Resource
    Electronic Resource
    Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 231-264 
    Details
    ISSN: 1573-2878
    Keywords: hierarchical control ; manufacturing systems ; stochastic dynamic programming ; optimal control ; long-run average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a production planning problem for a dynamic jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are assumed to be finite-state Markov chains. As the rates of change of the machine states approach infinity, an asymptotic analysis of this stochastic manufacturing systems is given. The analysis results in a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem is shown to converge to the long-run average cost of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem together with an error estimate for the constructed asymptotic optimal control is established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004667028547
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  • 10
    Electronic Resource
    Electronic Resource
    Some Optimal Control Problems Governed by Elliptic Variational Inequalities with Control and State Constraint on the Boundary (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 627-655 
    Details
    ISSN: 1573-2878
    Keywords: variational inequalities ; optimal control ; state constraint ; maximum principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This work deals with the necessary conditions of optimality for some optimal control problems governed by elliptic variational inequalities. Boundary control and state constrained problems are considered. The techniques used are based on those in Ref. 1 and a new penalty functional is defined in this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004613630675
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