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

Mathieu Claeys(mathieu.claeys***at***gmail.com)
Didier Henrion(henrion***at***laas.fr)
Martin Kruzik(kruzik***at***utia.cas.cz)

Abstract: Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phenomena, by relaxing controls as Young measures. These semi-definite relaxations were later on extended to optimal control problems depending linearly on the control 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 introduced originally by DiPerna and Majda in the partial differential equations literature 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 nonconvex optimal control problems with polynomial vector field and semialgebraic state constraints.

Keywords: optimal control; infinite-dimensional linear programming; semidefinite programming

Category 1: Applications -- Science and Engineering (Control Applications )

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation:

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Entry Submitted: 10/28/2014
Entry Accepted: 10/28/2014
Entry Last Modified: 10/28/2014

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