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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2017

Semi-definite relaxations for optimal control problems with oscillation and concentration effects

Résumé

Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phe-nomena, by relaxing controls as Young measures. These semi-definite relaxations were later on extended to optimal control problems depending linearly on the con-trol input and typically featuring concentration phenomena, interpreting the control as a measure of time with a discrete singular component modeling discontinuities or jumps of the state trajectories. In this contribution, we use measures intro-duced originally by DiPerna and Majda in the partial differential equations litera-ture to model simultaneously, and in a unified framework, possible oscillation and concentration effects of the optimal control policy. We show that hierarchies of semi-definite relaxations can also be constructed to deal numerically with noncon-vex optimal control problems with polynomial vector field and semialgebraic state constraints.
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Dates et versions

hal-01078217 , version 1 (28-10-2014)

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Mathieu Claeys, Didier Henrion, Martin Kružík. Semi-definite relaxations for optimal control problems with oscillation and concentration effects. ESAIM: Control, Optimisation and Calculus of Variations, 2017, 23 (1), pp.95-117. ⟨hal-01078217⟩
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