Existence of Neighboring Feasible Trajectories: Applications to Dynamic Programming for State-Constrained Optimal Control Problems |
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Authors: | H Frankowska R B Vinter |
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Institution: | (1) Centre de Recherche Viabilité, Jeux, Contrôle, CNRS and Université de Paris-Dauphine, Paris, France;(2) Centre for Process Systems Engineering and Department of Electrical and Electronic Engineering, Imperial College, London, UK |
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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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Keywords: | optimal control state constraints dynamic programming Hamilton-Jacobi equation |
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