HAL : hal-00723019, version 1

arXiv : 1208.1751

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Convex computation of the region of attraction of polynomial control systems

Didier Henrion 1, 2, Milan Korda 3

(07/08/2012)

We address the long-standing problem of computing the region of attraction (ROA) of a target set (typically a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We show that the ROA can be computed by solving a convex linear programming (LP) problem over the space of measures. In turn, this problem can be solved approximately via a classical converging hierarchy of convex finite-dimensional linear matrix inequalities (LMIs). Our approach is genuinely primal in the sense that convexity of the problem of computing the ROA is an outcome of optimizing directly over system trajectories. The dual LP on nonnegative continuous functions (approximated by polynomial sum-of-squares) allows us to generate a hierarchy of semialgebraic outer approximations of the ROA at the price of solving a sequence of LMI problems with asymptotically vanishing conservatism. This sharply contrasts with the existing literature which follows an exclusively dual Lyapunov approach yielding either nonconvex bilinear matrix inequalities or conservative LMI conditions.

1 :	Laboratoire d'analyse et d'architecture des systèmes (LAAS)
	CNRS : UPR8001 – Université Paul Sabatier [UPS] - Toulouse III – Institut National Polytechnique de Toulouse - INPT – Institut National des Sciences Appliquées (INSA) - Toulouse
2 :	Faculty of electrical engineering [Prague] (CTU/FEE)
	Czech Technical University in Prague
3 :	Ecole Polytechnique Fédérale de Lausanne (EPFL)
	École Polytechnique Fédérale de Lausanne

Équipe de recherche : Laboratoire dÁutomatique

Domaine

:

Mathématiques/Optimisation et contrôle

Mots Clés : Region of attraction – polynomial control systems – occupation measures – linear matrix inequalities (LMIs) – convex optimization – viability theory – capture basin.

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Contributeur : Didier Henrion <>

Soumis le : Mardi 7 Août 2012, 10:08:38

Dernière modification le : Lundi 17 Septembre 2012, 13:49:53