Quadratic Optimal Control of Linear Complementarity Systems: First order necessary conditions and numerical analysis

Commande optimale quadratique des Systèmes de Complémentarité Linéaire : conditions nécessaires du premier ordre, analyse numérique

Alexandre Vieira (1) , Bernard Brogliato (1) , Christophe Prieur (2)

1 TRIPOP - Modélisation, simulation et commande des systèmes dynamiques non lisses
2 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics

This article is dedicated to the analysis of quadratic optimal control of linear complementarity systems (LCS), which are a class of strongly nonlinear and nonsmooth dynamical systems. Necessary first-order conditions are derived, that take the form of an LCS with inequality constraints, hence are numerically tractable. Sufficiency is proved in a specific sense. Numerical examples illustrate the theoretical developments and demonstrate the efficiency of the complementarity approach.

Mots clés: Optimal control; Indexes; Numerical analysis; Nash equilibrium; Games; Contacts

Domaines: Systèmes et contrôle [cs.SY]; Automatique; Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Alexandre Vieira, Bernard Brogliato, Christophe Prieur. Quadratic Optimal Control of Linear Complementarity Systems: First order necessary conditions and numerical analysis. IEEE Transactions on Automatic Control, 2020, 65 (6), pp.2743-2750. ⟨10.1109/TAC.2019.2945878⟩. ⟨hal-01690400v3⟩