Existence of Neighboring Feasible Trajectories: Applications to Dynamic Programming for State-Constrained Optimal Control Problems

H. Frankowska and R. B. Vinter
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H. Frankowska: CNRS and Université de Paris-Dauphine
R. B. Vinter: Imperial College

Journal of Optimization Theory and Applications, 2000, vol. 104, issue 1, No 3, 20-40

Abstract: 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.

Keywords: optimal control; state constraints; dynamic programming; Hamilton-Jacobi equation (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1004668504089

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