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1.
Consider a differential inclusion under state constraints
where is an unbounded set-valued map with closed and convex images, which is measurable in and -Lipschitz in (with ) and is a closed set with smooth boundary. We provide sufficient conditions for the set-valued map associating to each initial point the set of all solutions to the above constrained differential inclusion starting at to be pseudo-Lipschitz on . This result is applied to investigate local Lipschitz continuity of the value function for the constrained Bolza problem
of optimal control theory.
Work supported in part by the European Community's Human Potential Programme under contract HPRN-CT-2002-00281, Evolution
Equations. 相似文献
2.
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. 相似文献
3.
A theoretical sensitivity analysis for parametric optimal control problems subject to pure state constraints has recently been elaborated in [7,8]. The articles consider both first and higher order state constraints and develop conditions for solution differentiability of optimal solutions with respect to parameters. In this paper, we treat the numerical aspects of computing sensitivity differentials via appropriate boundary value problems. In particular, numerical methods are proposed that allow to verify all assumptions underlying solution differentiability. Three numerical examples with state constraints of order one, two and four are discussed in detail. 相似文献