Nonlinear optimal control via occupation measures and LMI-relaxations

Jean-Bernard Lasserre (1) , Didier Henrion (1) , Christophe Prieur (1) , Emmanuel Trélat (2)

1 LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control con- straints and cost are all described by polynomials, and more generally for OCPs with smooth data. In addition, state constraints as well as state and/or action constraints are allowed. We provide a simple hierarchy of LMI (lin- ear matrix inequality)-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Under some convexity assump- tions, the sequence converges to the optimal value of the OCP. Preliminary results show that good approximations are obtained with few moments.

Mots clés: Nonlinear control; Optimal control; Semidefinite Programming; Measures; Moments

Domaines: Optimisation et contrôle [math.OC]

Jean-Bernard Lasserre, Didier Henrion, Christophe Prieur, Emmanuel Trélat. Nonlinear optimal control via occupation measures and LMI-relaxations. 2007. ⟨hal-00136032v1⟩