139,969 research outputs found

    Optimal Control Problems with Mixed and Pure State Constraints

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    This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both “pure” constraints on the state variable and “mixed” constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constraint problems, according to which Clarke's theory of “stratified” necessary conditions is applied to a modified optimal control problem resulting from absorbing the mixed constraint into the dynamics; the difference here is that necessary conditions which now take into account the presence of pure state constraints are applied to the modified problem. Necessary conditions are given for a rather general formulation of the problem containing both forms of the constraints, and then these are specialized to problems having special structure. While combined pure state and mixed control/state problems have been previously treated in the literature, the necessary conditions in this paper are proved under less restrictive hypotheses and for novel formulations of the constraints

    Optimal Control Problems with Mixed and Pure State Constraints

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    This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both ‘pure’ constraints on the state variable and also ‘mixed’ constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constraint problems, according to which Clarke’s theory of ‘stratified’ necessary conditions is applied to a modified optimal control problem resulting from absorbing the mixed constraint into the dynamics; the difference here is that necessary conditions which now take account of the presence of pure state constraints are applied to the modified problem. Necessary conditions are given for a rather general formulation of the problem containing both forms of the constraints, and then these are specialized to apply to problems having special structure. While combined pure state and mixed control/state problems have been previously treated in the literature, the necessary conditions in this paper are proved under less restrictive hypotheses and for novel formulations of the constraints

    A special class of mixed constrained optimal control problems

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    The focus of this paper is on optimal control problems with mixed state and control inequality constraints. We identify a class of problems which can be associated with an auxiliary problem with both regular mixed constraints and pure state constraints. For that class of problems we derive a new set of necessary conditions of optimality. © 2007 EUCA

    A MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL PROBLEMS WITH STATE AND MIXED CONSTRAINTS

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    Here we derive a variant of the nonsmooth maximum principle for optimal control problems with both pure state and mixed state and control constraints. Our necessary conditions include a Weierstrass condition together with an Euler adjoint inclusion involving the joint subdifferentials with respect to both state and control, generalizing previous results in [M.d.R. de Pinho, M.M.A. Ferreira, F.A.C.C. Fontes, Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems. ESAIM: COCV 11 (2005) 614-632]. A notable feature is that our main results are derived combining old techniques with recent results. We use a well known penalization technique for state constrained problem together with an appeal to a recent nonsmooth maximum principle for problems with mixed constraints

    Interior Point Methods in Optimal Control

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    This paper deals with Interior Point Methods (IPMs) for Optimal Control Problems (OCPs) with pure state and mixed constraints. This paper establishes a complete proof of convergence of IPMs for a general class of OCPs. Convergence results are proved for primal variables, namely state and control variables, and for dual variables, namely, the adjoint state, and the constraints multipliers. In addition, the presented convergence result does not rely on a strong convexity assumption. Finally, this paper provides two IPM-based solving algorithms: a primal solving algorithm and a primal-dual solving algorithm.Comment: arXiv admin note: substantial text overlap with arXiv:2308.1655

    Second-order necessary conditions in Pontryagin form for optimal control problems

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    International audienceIn this report, we state and prove first- and second-order necessary conditions in Pontryagin form for optimal control problems with pure state and mixed control-state constraints. We say that a Lagrange multiplier of an optimal control problem is a Pontryagin multiplier if it is such that Pontryagin's minimum principle holds, and we call optimality conditions in Pontryagin form those which only involve Pontryagin multipliers. Our conditions rely on a technique of partial relaxation, and apply to Pontryagin local minima.Dans ce rapport, nous énonçons et prouvons des conditions nécessaires du premier et second ordre sous forme Pontryaguine pour des problèmes de commande optimale avec contraintes pures sur l'état et mixtes sur l'état et la commande. Nous appelons multiplicateur de Pontryaguine tout multiplicateur de Lagrange pour lequel le principe de Pontryaguine est satisfait et parlons de conditions d'optimalité sous forme Pontryaguine si elles ne font intervenir que des multiplicateurs de Pontryaguine. Nos conditions s'appuient sur une technique de relaxation partielle et sont valables pour des minima de Pontryaguine

    A Nonsmooth Maximum Principle for Optimal Control Problems with State and Mixed Constraints-Convex Case

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    Here we derive a nonsmooth maximum principle for optimal control problems with both state and mixed constraints. Crucial to our development is a convexity assumption on the "velocity set". The approach consists of applying known penalization techniques for state constraints together with recent results for mixed constrained problems.Comment: Published in 'Discrete and Continuous Dynamical Systems, Vol. 2011, pp. 174-18
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