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  • optimal control
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  • Springer  (40)
  • Wiley-Blackwell  (1)
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  • American Physical Society
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  • 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
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    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
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    Numerical Schemes for Discontinuous Value Functions of Optimal Control (2000)
    Springer
    Set-valued analysis 8 (2000), S. 111-126 
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    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
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    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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  • 7
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    Nonlinear Potentials for Hamilton–Jacobi–Bellman Equations. II (1997)
    Springer
    Acta applicandae mathematicae 46 (1997), S. 29-48 
    Details
    ISSN: 1572-9036
    Keywords: Hamilton–Jacobi–Bellman equations ; nonlinear potentials ; nonlinear PDE ; viscosity solutions ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A formal method of constructing the viscosity solutions for abstract nonlinear equations of Hamilton–Jacobi–Bellman (HJB) type was developed in the previous work of the author. A new advantage of this method (which was called an ‘nonlinear potentials’ method) is that it gives a possibility to choose at the first step an expected regularity of the solution and then – to construct this solution. This makes the whole procedure more simple because an analysis of regularity of viscosity solutions is usually the most complicated step. Nonlinear potentials method is a generalization of Krylov's approach to study HJB equations. In this article nonlinear potentials method is applied to elliptic degenerate HJB equations in Rd with variable coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005786132384
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  • 8
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    Topological properties of the solution set of a class of nonlinear evolutions inclusions (1997)
    Springer
    Czechoslovak mathematical journal 47 (1997), S. 409-424 
    Details
    ISSN: 1572-9141
    Keywords: R δ-set ; homotopic ; contractible ; evolution triple ; evolution inclusion ; compact embedding ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field F(t, x), we are able to show that the solution set is in fact an R δ-set. Finally some applications to infinite dimensional control systems are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022451115373
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  • 9
    Electronic Resource
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    On the existence of optimal controls for nonlinear infinite dimensional systems (1998)
    Springer
    Czechoslovak mathematical journal 48 (1998), S. 291-312 
    Details
    ISSN: 1572-9141
    Keywords: evolution triple ; optimal control ; monotone operator ; hemicontinuous operator ; parabolic system ; property (Q)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022889404413
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  • 10
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    The optimal control variational principle and finite elements analysis for viscoplastic dynamics (1997)
    Springer
    Applied mathematics and mechanics 18 (1997), S. 61-68 
    Details
    ISSN: 1573-2754
    Keywords: viscoplastic dynamics ; optimal control ; variational principle ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper presents the optimal control variational principle for Perzyna model which is one of the main constitutive relation of viscoplasticity in dynamics. And it could also be transformed to solve the parametric quadratic programming problem. The FEM form of this problem and its implementation have also been discussed in the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02457502
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  • 11
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    Scheduling Under Common Due Date, A Single Resource and Precedence Constraints—A Dynamic Approach (1998)
    Springer
    Discrete event dynamic systems 8 (1998), S. 353-364 
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    ISSN: 1573-7594
    Keywords: scheduling ; optimal control ; time-decomposition methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper discusses dynamic methods for solving a class of multi-project scheduling problems in which rates of job performances are controllable and resources such as money, energy or manpower per time unit, are renewable and continuously divisible. The objective is to complete the projects as close to the common due date as possible. Two different ways of imposing sequential precedence relations between project jobs are explored by formulating two dynamic models and studying their relationships on the optimal solution. Efficient time-decomposition algorithms for finding either globally optimal schedules or lower bound guided near-optimal solutions are suggested and computationally tested.
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    URL: http://dx.doi.org/10.1023/A:1008345132480
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  • 12
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    Modeling, Analysis, and Optimal Control of a Class of Hybrid Systems (1998)
    Springer
    Discrete event dynamic systems 8 (1998), S. 175-201 
    Details
    ISSN: 1573-7594
    Keywords: hybrid systems ; optimal control ; calculus of variations ; manufacturing systems ; queueing systems ; nonsmooth optimization ; two point boundary value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We propose a modeling framework for a class of hybrid systems which arise in many manufacturing environments and study related optimal control problems. In this framework, discrete entities have a state characterized by a temporal component whose evolution is described by event-driven dynamics, and a physical component whose evolution is described by time-driven dynamics. As a first step towards developing an optimal control theory for such hybrid systems, we formulate a problem consisting of a single-stage manufacturing process and use calculus of variations techniques to obtain structural properties and an explicit algorithm for deriving optimal policies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008237701804
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  • 13
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    Optimal Production Planning in a Multi-Product Stochastic Manufacturing System with Long-Run Average Cost (1998)
    Springer
    Discrete event dynamic systems 8 (1998), S. 37-54 
    Details
    ISSN: 1573-7594
    Keywords: Production planning ; stochastic dynamic programming ; vanishing discount approach ; optimal control ; long-run average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the problem of production planning in a flexible manufacturing system consisting of a single or parallel failure-prone machines producing a number of different products. The objective is to choose the rates of production of the various products over time in order to meet their demands at the minimum long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach for the average cost problem that the Hamilton-Jacobi-Bellman equation in terms of directional derivatives has a solution consisting of the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem, and in specifying an optimal control policy in terms of the potential function. The results settle a hitherto open problem as well as generalize known results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008256409920
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  • 14
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    Maximum Principle for a Control Problem Governed by an Evolution Equation (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 263-276 
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    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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  • 15
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    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 
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    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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  • 16
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    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 
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    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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  • 17
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    Instabilities in Concave, Dynamic, Economic Optimization (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 275-286 
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    ISSN: 1573-2878
    Keywords: optimal control ; thresholds ; multiple equilibria ; instability ; concavity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An important and numerous literature argues that nonconcavity (often convexity with respect to the state) of the Hamiltonian leads to multiple steady states, instability, and a threshold. This threshold property provides a powerful paradigm to explain history dependency and hysteresis. This paper shows that economically relevant properties (in particular, multiple steady states and thresholds) are possible in strict concave models too. Two corresponding necessary conditions with intuitive economic interpretation are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026408814862
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  • 18
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    Convergence of Solutions to Equations Arising in Neural Networks (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 533-560 
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    ISSN: 1573-2878
    Keywords: Polynomial differential equations ; convergence of solutions ; neural network systems ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study polynomial ordinary differential systems $$\dot M(t) = QM - M(M'QM){\text{, }}M(0) = M_0 ,t \geqslant 0,$$ whereQ≥0 is an n×n matrix and M(t) is an n×k matrix. It is proven that, as t grows to infinity, the solution M(t) tends to a limit BU, where U is a k×k orthogonal matrix and B is an n×k matrix whose columns are k pairwise orthogonal, normalized eigenvectors of Q. Moreover, for almost every M 0, these eigenvectors correspond to the k maximal eigenvalues of Q; for an arbitrary Q with independent columns, we provide a procedure of computing B by employing elementary matrix operations on M 0. This result is significant for the study of certain neural network systems, and in this context it shows that M(∞) provides a principal component analyzer.
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    URL: http://dx.doi.org/10.1023/A:1022633615273
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  • 19
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    Mixed Frank–Wolfe Penalty Method with Applications to Nonconvex Optimal Control Problems (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 311-334 
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    ISSN: 1573-2878
    Keywords: Mixed penalty method ; Frank–Wolfe method ; optimal control ; relaxed control ; lumped systems ; distributed systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a general optimization problem which is an abstract formulation of a broad class of state-constrained optimal control problems in relaxed form. We describe a generalized mixed Frank–Wolfe penalty method for solving the problem and prove that, under appropriate assumptions, accumulation points of sequences constructed by this method satisfy the necessary conditions for optimality. The method is then applied to relaxed optimal control problems involving lumped as well as distributed parameter systems. Numerical examples are given.
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    URL: http://dx.doi.org/10.1023/A:1022631611812
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  • 20
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    In Optimal Control Problem in Economics with Four Linear Controls (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 619-634 
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    ISSN: 1573-2878
    Keywords: Microeconomic models ; optimal control ; linear controls ; singular subarcs ; necessary conditions ; minimum principle as LP ; direct collocation method ; indirect multiple shooting method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An optimal control problem with four linear controls describing a sophisticated concern model is investigated. The numerical solution of this problem by combination of a direct collocation and an indirect multiple shooting method is presented and discussed. The approximation provided by the direct method is used to estimate the switching structure caused by the four controls occurring linearly. The optimal controls have bang-bang subarcs as well as constrained and singular subarcs. The derivation of necessary conditions from optimal control theory is aimed at the subsequent application of an indirect multiple shooting method but is also interesting from a mathematical point of view. Due to the linear occurrence of the controls, the minimum principle leads to a linear programming problem. Therefore, the Karush–Kuhn–Tucker conditions can be used for an optimality check of the solution obtained by the indirect method.
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    URL: http://dx.doi.org/10.1023/A:1022648900252
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  • 21
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    Approximate Solutions to the Time-Invariant Hamilton–Jacobi–Bellman Equation (1998)
    Springer
    Journal of optimization theory and applications 96 (1998), S. 589-626 
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    ISSN: 1573-2878
    Keywords: Nonlinear control ; optimal control ; Hamilton–Jacobi–Bellman equation ; feedback synthesis ; successive approximation ; Galerkin approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we develop a new method to approximate the solution to the Hamilton–Jacobi–Bellman (HJB) equation which arises in optimal control when the plant is modeled by nonlinear dynamics. The approximation is comprised of two steps. First, successive approximation is used to reduce the HJB equation to a sequence of linear partial differential equations. These equations are then approximated via the Galerkin spectral method. The resulting algorithm has several important advantages over previously reported methods. Namely, the resulting control is in feedback form and its associated region of attraction is well defined. In addition, all computations are performed off-line and the control can be made arbitrarily close to optimal. Accordingly, this paper presents a new tool for designing nonlinear control systems that adhere to a prescribed integral performance criterion.
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    URL: http://dx.doi.org/10.1023/A:1022664528457
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    Robust Stabilization for a Class of Uncertain Nonlinear Systems with Time-Varying Delay: Razumikhin-Type Approach (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 161-173 
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    ISSN: 1573-2878
    Keywords: Robust stabilization ; optimal control ; time-delay systems ; Razumikhin-type approach
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, using a Razumikhin-type approach, the stabilization of a class of uncertain nonlinear systems with time-varying delay is considered. The proposed controller is based on a specific optimal control problem. Global asymptotic stability is guaranteed for the proposed control if some algebraic condition is met. An example illustrates the use of the main result.
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    URL: http://dx.doi.org/10.1023/A:1022645116123
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    Based on wavelet analysis to optimal control of motion planning of space manipulator (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 1161-1168 
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    ISSN: 1573-2754
    Keywords: space manipulator ; motion planning ; optimal control ; wavelet analysis ; TP241
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The optimal control problem of nonholonomic motion planning of space manipulator was discussed. Utilizing the method of wavelet analysis, the discrete orthogonal wavelets were introduced to solve the optimal control problem, the classical Fourier basic functions were replaced by the wavelet expansion approximation. A numerical algorithm of optimal control was proposed based on wavelet analysis. The numerical simulation shows, the method is effective for nonholonomic motion planning of space manitulator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458994
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    Optimization of Bilinear Systems Using a Higher-Order Variational Method (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 55-72 
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    ISSN: 1573-2878
    Keywords: optimal control ; bilinear systems ; nilpotent Lie algebra ; products of exponentials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper derives some optimization results for bilinear systems using a higher-order method by characterizing them over matrix Lie groups. In the derivation of the results, first a bilinear system is transformed to a left-invariant system on matrix Lie groups. Then, the product of exponential representation is used to express this system in canonical form. Next, the conditions for optimality are obtained by the principles of variational calculus. It is demonstrated that closed-form analytical solutions exist for classes of bilinear systems whose Lie algebra are nilpotent.
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    URL: http://dx.doi.org/10.1023/A:1004609911204
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  • 25
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    Optimal Expenditure Patterns of a Double-Path Engineering Project (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 441-455 
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    ISSN: 1573-2878
    Keywords: expenditure patterns ; research and development ; optimal control ; calculus of variations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The optimal expenditure pattern for a double-path engineering project, i.e., a project composed of a nonroutine risky R&D path and a routine nonrisky preparatory path, manufacturing related or marketing related, is studied via the calculus of variations to derive a set of twin second-order nonlinear differential equations whose solution yields the optimal joint expenditure. Assuming independence between the risky and nonrisky paths, a constant return per unit time, a gamma-type unimodal conditional-completion density function for the R&D activity, and the principle of diminishing returns on the effort, we find an interesting interplay between the two paths for the peak position and termination of the expenditures. Counterintuitively, we find that the peak expenditure of the R&D path does not necessarily precede that of the preparatory path, although both path expenditure peaks obey the well-known Kamien–Schwartz theorem. That is, for both paths, the expenditure peak positions precede always the peak of the conditional-completion density function of the R&D path.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004670120484
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    Universal Near-Optimal Feedbacks (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 89-122 
    Details
    ISSN: 1573-2878
    Keywords: optimal control ; differential games ; Euler polygonal arcs ; nonsmooth analysis ; proximal aiming ; infinitesimal decrease ; discontinuous universal near-optimal feedback
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a general fixed-duration optimal control problem, the proximal aiming technique of nonsmooth analysis is employed in order to construct a discontinuous feedback law, whose Euler solutions are all optimal to within a prescribed tolerance, universally for all initial data in a prescribed bounded set. The technique is adapted in order to construct universal near-saddle points for two-player fixed-duration differential games of the Krasovskii–Subbotin type.
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    URL: http://dx.doi.org/10.1023/A:1004608800846
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    Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost (1997)
    Springer
    Journal of optimization theory and applications 92 (1997), S. 161-188 
    Details
    ISSN: 1573-2878
    Keywords: Production planning ; stochastic dynamic programming ; vanishing discount approach ; optimal control ; long-run average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the optimal production planning in a dynamic stochastic manufacturing system consisting of a single machine that is failure prone and facing a constant demand. The objective is to choose the rate of production over time in order to minimize the long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach that the Hamilton–Jacobi–Bellman equation for the average cost problem has a solution giving rise to the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem. Finally, the optimal control policy is specified in terms of the potential function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022696215389
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    ℓ1-Minimization with Magnitude Constraints in the Frequency Domain (1997)
    Springer
    Journal of optimization theory and applications 93 (1997), S. 27-51 
    Details
    ISSN: 1573-2878
    Keywords: Robust control ; multiobjective control ; optimal control ; $$\ell _1 $$ –control ; computational methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we study the $$\ell _1 $$ -optimal control problem with additional constraints on the magnitude of the closed-loop frequency response. In particular, we study the case of magnitude constraints at fixed frequency points (a finite number of such constraints can be used to approximate an $$H_\infty $$ -norm constraint). In previous work, we have shown that the primal-dual formulation for this problem has no duality gap and both primal and dual problems are equivalent to convex, possibly infinite-dimensional, optimization problems with LMI constraints. Here, we study the effect of approximating the convex magnitude constraints with a finite number of linear constraints and provide a bound on the accuracy of the approximation. The resulting problems are linear programs. In the one-block case, both primal and dual programs are semi-infinite dimensional. The optimal cost can be approximated, arbitrarily well from above and within any predefined accuracy from below, by the solutions of finite-dimensional linear programs. In the multiblock case, the approximate LP problem (as well as the exact LMI problem) is infinite-dimensional in both the variables and the constraints. We show that the standard finite-dimensional approximation method, based on approximating the dual linear programming problem by sequences of finite-support problems, may fail to converge to the optimal cost of the infinite-dimensional problem.
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    URL: http://dx.doi.org/10.1023/A:1022641516007
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    Dynamic Sampling Applied to Problems in Optimal Control (1997)
    Springer
    Journal of optimization theory and applications 95 (1997), S. 565-580 
    Details
    ISSN: 1573-2878
    Keywords: Brownian motion ; diffusion processes ; observers ; dynamic sampling ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Dynamic sampling utilizes the option of varying the sampling rates according to the situation of the systems, thus obtaining procedures with improved efficiencies. In this paper, the technique is applied to a typical problem in optimal control theory, that of tracking and controlling the position of an object. It is shown that the dynamic sampling results in a significantly improved procedure for this case, even when applying a suboptimal policy which can be analyzed in closed form.
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    URL: http://dx.doi.org/10.1023/A:1022669821575
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    Optimal Control of Rigid Body Angular Velocity with Quadratic Cost (1998)
    Springer
    Journal of optimization theory and applications 96 (1998), S. 507-532 
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    ISSN: 1573-2878
    Keywords: Rigid bodies ; Hamilton–Jacobi equation ; Riccati equation ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the problem of obtaining optimal controllers which minimize a quadratic cost function for the rotational motion of a rigid body. We are not concerned with the attitude of the body and consider only the evolution of the angular velocity as described by the Euler equations. We obtain conditions which guarantee the existence of linear stabilizing optimal and suboptimal controllers. These controllers have a very simple structure.
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    URL: http://dx.doi.org/10.1023/A:1022656326640
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    Optimization of a Class of Nonlinear Dynamic Systems: New Efficient Method without Lagrange Multipliers (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 11-28 
    Details
    ISSN: 1573-2878
    Keywords: Optimization ; nonlinear dynamic systems ; transformations ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with optimization of a class of nonlinear dynamic systems with n states and m control inputs commanded to move between two fixed states in a prescribed time. Using conventional procedures with Lagrange multipliers, it is well known that the optimal trajectory is the solution of a two-point boundary-value problem. In this paper, a new procedure for dynamic optimization is presented which relies on tools of feedback linearization to transform nonlinear dynamic systems into linear systems. In this new form, the states and controls can be written as higher derivatives of a subset of the states. Using this new form, it is possible to change constrained dynamic optimization problems into unconstrained problems. The necessary conditions for optimality are then solved efficiently using weighted residual methods.
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    URL: http://dx.doi.org/10.1023/A:1022666831628
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    Optimal Control of a Stochastic Assembly Production Line (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 681-700 
    Details
    ISSN: 1573-2878
    Keywords: Manufacturing systems ; bang–bang control ; dynamic programming ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The system under consideration comprises n workstations in parallel and one assembly workstation. The workstations are either reliable or unreliable and the product demand is random. The n different type parts are processed first in the parallel workstations and then are joined in the assembly workstation. By minimizing the expected discounted cost, it is shown that the optimal control policy is of the bang–bang type and can be described by a set of switching manifolds. The structural properties of the optimal policy, such as monotonicity and asymptotic behavior, are investigated. These structural properties are very useful to find the optimal policy in large-size systems. Three numerical examples are given to demonstrate the results.
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    URL: http://dx.doi.org/10.1023/A:1022632231356
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    Finite-Time Optimal Control of Polynomial Systems Using Successive Suboptimal Approximations (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 477-489 
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    ISSN: 1573-2878
    Keywords: optimal control ; polynomial systems ; quasilinearization ; successive approximation ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown in this paper that the finite-time optimal control of polynomial systems can be obtained by solving a sequence of optimal control problems for the linearized problem. The paper provides proof of convergence as well as illustration of the procedure by two examples.
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    URL: http://dx.doi.org/10.1023/A:1004674221393
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    Stochastic Games for N Players (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 543-565 
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    ISSN: 1573-2878
    Keywords: stochastic games ; dynamic programming ; optimal control ; regularity theory ; Nash point
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The objective of this paper is to present a useful application of the theory of regularity of systems of nonlinear partial differential equations to the solution of stochastic differential games with N players. It is particularly interesting to notice that the structure of games fits perfectly with what is requested to prove the regularity property which is needed.
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    URL: http://dx.doi.org/10.1023/A:1004637022496
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    Existence of Neighboring Feasible Trajectories: Applications to Dynamic Programming for State-Constrained Optimal Control Problems (2000)
    Springer
    Journal of optimization theory and applications 104 (2000), S. 20-40 
    Details
    ISSN: 1573-2878
    Keywords: optimal control ; state constraints ; dynamic programming ; Hamilton-Jacobi equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semicontinuous generalized solution of the Hamilton-Jacobi equation. This is achieved under a constraint qualification (CQ) concerning the interaction of the state and dynamic constraints. The novelty of the results reported here is partly the nature of (CQ) and partly the proof techniques employed, which are based on new estimates of the distance of the set of state trajectories satisfying a state constraint from a given trajectory which violates the constraint.
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    URL: http://dx.doi.org/10.1023/A:1004668504089
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    Optimal Control Problem for the Lyapunov Exponents of Random Matrix Products (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 347-369 
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    ISSN: 1573-2878
    Keywords: random matrix products ; Lyapunov exponents ; Markov processes ; decision models ; optimal policy ; optimal control ; system spectrum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with the optimal control problem for the Lyapunov exponents of stochastic matrix products when these matrices depend on a controlled Markov process with values in a finite or countable set. Under some hypotheses, the reduced process satisfies the Doeblin condition and the existence of an optimal control is proved. Furthermore, with this optimal control, the spectrum of the system consists of only one element.
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    URL: http://dx.doi.org/10.1023/A:1004661918667
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    Bilinear Control and Application to Flexible a.c. Transmission Systems (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 621-637 
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    ISSN: 1573-2878
    Keywords: bilinear systems ; optimal control ; controllability ; stabilization ; electric power
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this paper is an integrated overview of bilinear systems (BLS) research which has evolved over the past few decades, and a new result on control of flexible a.c. transmission systems (FACTS) is presented. BLS may be derived in many cases from principles of physics, chemistry, biology, socioeconomics, and engineering. In other cases, BLS are more accurate approximations to nonlinear systems than are traditional linear systems, as shown for example by the added bilinear terms (in state and control) for the Taylor series. While an appropriately designed linear control system may be optimum relative to some quadratic performance index without added constraints, bilinear or parametric control can be designed to improve more global performance and indeed to increase the region of attainable states. Such controllability and stabilization of BLS and of a series line-capacitor controlled FACTS is presented.
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    URL: http://dx.doi.org/10.1023/A:1004645224313
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    Application of Stochastic Global Optimization Algorithms to Practical Problems (1997)
    Springer
    Journal of optimization theory and applications 95 (1997), S. 545-563 
    Details
    ISSN: 1573-2878
    Keywords: Global optimization ; real life problems ; pig liver likelihood function ; many-body potential function ; tank reactor ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We describe global optimization problems from three different fields representing many-body potentials in physical chemistry, optimal control of a chemical reactor, and fitting a statistical model to empirical data. Historical background for each of the problems as well as the practical significance of the first two are given. The problems are solved by using eight recently developed stochastic global optimization algorithms representing controlled random search (4 algorithms), simulated annealing (2 algorithms), and clustering (2 algorithms). The results are discussed, and the importance of global optimization in each respective field is focused.
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    URL: http://dx.doi.org/10.1023/A:1022617804737
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    Optimal Control of a Ship for a Course-Changing Maneuver (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 281-297 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear ship steering dynamics ; optimal control ; saturation ; slew rate limitation ; sequential gradient-restoration algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The steering control of a ship during a course-changing maneuver is formulated as a Bolza optimal control problem, which is solved via the sequential gradient-restoration algorithm (SGRA). Nonlinear differential equations describing the yaw dynamics of a steering ship are employed as the differential constraints, and both amplitude and slew rate limits on the rudder are imposed. Two performance indices are minimized: one measures the time integral of the squared course deviation between the actual ship course and a target course; the other measures the time integral of the absolute course deviation. Numerical results indicate that a smooth transition from the initial set course to the target course is achievable, with a trade-off between the speed of response and the amount of course angle overshoot.
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    URL: http://dx.doi.org/10.1023/A:1022674516570
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    Solution of Fixed Final State Optimal Control Problems via Simple Cell Mapping (2000)
    Springer
    Nonlinear dynamics 23 (2000), S. 391-403 
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    ISSN: 1573-269X
    Keywords: optimal control ; cell mapping method ; dynamic programing ; parametric control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A strategy is proposed to solve the fixed final state optimalcontrol problem using the simple cell mapping method. A non-uniform timestep simple cell mapping is developed to create a general database fromwhich solutions of various optimal control problems can be obtained. Atwo-stage backward search algorithm is proposed to eliminate degeneratedpaths often associated with the simple cell mapping. The proposed methodcan accurately delineate the switching curves and eliminate false limitcycles in the solution. The method is applied to two optimal controlproblems with bang-bang control. The well-known minimum time controlproblem of moving a point mass from any initial condition to the originof the phase plane is studied first. This example has exact solutionsavailable which provide a yardstick to examine the accuracy of themethod. The cell size dependence of the solution accuracy is studiednumerically. The second example is a variable stiffness feedback controlproblem with tuning range saturation. The strategy proposed is able toprovide the switching curves in the phase plane. This result has notbeen obtained before.
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    URL: http://dx.doi.org/10.1023/A:1008375230648
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    Solving boundary-value problems using hp-version finite elements in time (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 425-440 
    Details
    ISSN: 0029-5981
    Keywords: numerical methods ; time-marching ; dynamics ; optimal control ; boundary-value problems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An hp-version finite element method for one-dimensional boundary value problems is presented. The method is based on a similar approach developed by the authors for solution of optimal control problems. The primary applications for the methodology include two-point- and multi-point-boundary-value problems, for example, in the time domain. Results presented for a 7-state/3-phase missile problem show that the method is very efficient for time-marching applications. Furthermore, it easily solves time-domain problems with discontinuities in the system equations and/or in the states, where the time at which these jumps (i.e. ‘events’) take place is determined by equations that govern the states. An example involving friction with intermittent sticking is presented to illustrate the power of the method. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
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