On the Computation of Set-Induced Control Lyapunov Functions for Continuous-Time Systems

Mirko Fiacchini (1) , Christophe Prieur (1) , Sophie Tarbouriech (2)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

The paper presents a computation-oriented method for characterizing and obtaining local control Lyapunov functions induced by particular star-shaped nonconvex sets for continuous-time nonlinear systems with bounded inputs. For a given set, the necessary and sufficient conditions for the induced function to be a nonconvex local control Lyapunov function are provided. The related convex problems for computing the exact region in which the function is decreasing and the optimal control input are presented. The results are applied to the Brockett integrator.

Mots clés: nonlinear systems; convex analysis; viability theory; invariant sets

Domaines: Systèmes dynamiques [math.DS]

Mirko Fiacchini, Christophe Prieur, Sophie Tarbouriech. On the Computation of Set-Induced Control Lyapunov Functions for Continuous-Time Systems. SIAM Journal on Control and Optimization, 2015, 53 (3), pp.1305-1327. ⟨10.1137/130934908⟩. ⟨hal-01133446⟩