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Linear conic optimization for nonlinear optimal control

Didier Henrion(henrion***at***laas.fr)
Edouard Pauwels(pauwelsed***at***gmail.com)

Abstract: Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual linear problem consists of finding the largest lower bound on the value function of the optimal control problem. Various approximation results relating the original optimal control problem and its linear conic formulations are developed. As illustrated by a couple of simple examples, these results are relevant in the context of finite-dimensional semidefinite programming relaxations used to approximate numerically the solutions of the infinite-dimensional linear conic problems.

Keywords: optimal control; linear programming; semidefinite programming

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

Category 2: Infinite Dimensional Optimization (Other )

Category 3: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: Submitted for possible inclusion as a contributed chapter in S. Ahmed, M. Anjos, T. Terlaky (Editors). Advances and Trends in Optimization with Engineering Applications. MOS-SIAM series, SIAM, Philadelphia.

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Entry Submitted: 07/07/2014
Entry Accepted: 07/07/2014
Entry Last Modified: 07/07/2014

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