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Reports (Research Report) Year : 2006

Some results on the optimal control with unilateral state constraints

Abstract

In this paper we study the problem of quadratic optimal control with state variables unilateral constraints, for linear time-invariant systems. The necessary conditions are formulated as a linear invariant system with complementary slackness conditions. Some structural properties of this system are examined. Then it is shown that the problem can benefit from the higher order Moreau's sweeping process, that is a specific distributional differential inclusion, and from ten Dam's geometric theory for the partitioning of the admissible domain boundary. In fact the first step may be also seen as follows: does the higher order Moreau's sweeping process (developed in \cite{VA-BB-DG,JJ2003}) correspond to the necessary conditions of some optimal control problem with an adapted integral action? The knowledge of the qualitative behaviour of optimal trajectories is improved with the approach, which also paves the way towards efficient time-stepping numerical algorithms to solve the optimal control boundary value problem.
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Dates and versions

inria-00103775 , version 1 (12-10-2006)
inria-00103775 , version 2 (12-10-2006)

Identifiers

  • HAL Id : inria-00103775 , version 2

Cite

Bernard Brogliato. Some results on the optimal control with unilateral state constraints. [Research Report] RR-5992, INRIA. 2006. ⟨inria-00103775v2⟩
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