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Nonlinear optimal control: Numerical approximations via moments and LMI-relaxations

Jean B. Lasserre (lasserre***at***laas.fr)
Christophe Prieur (cprieur***at***laas.fr)
Didier Henrion (henrion***at***laas.fr)

Abstract: We consider the class of nonlinear optimal control problems with all data (differential equation, state and control constraints, cost) being polynomials. We provide a simple hierarchy of LMI-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Preliminary results show that good approximations are obtained with few moments.

Keywords: Nonlminear optimal control; LMI-relaxations

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 2: Applications -- Science and Engineering (Control Applications )

Citation: LAAS report 05120, March 2005, Toulouse, France. To appear in Proceedings of the IEEE CDC Conference, Sevilla, Spain, December 2005.

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Entry Submitted: 09/23/2005
Entry Accepted: 09/23/2005
Entry Last Modified: 09/23/2005

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