On Barriers in State and Input Constrained Nonlinear Systems

José A de Doná (1) , Jean Lévine (2)

1 School of Electrical Engineering and Computer Science
2 CAS - Centre Automatique et Systèmes

In this paper, the problem of state and input constrained control is addressed, with multidimensional constraints. We obtain a local description of the boundary of the admissible subset of the state space where the state and input constraints can be satisfied for all times. This boundary is made of two disjoint parts: the subset of the state constraint boundary on which there are trajectories pointing towards the interior of the admissible set or tangentially to it; and a barrier, namely a semipermeable surface which is constructed via a minimum-like principle.

Mots clés: state and input constraints; barrier; admissible set; nonlinear systems

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

José A de Doná, Jean Lévine. On Barriers in State and Input Constrained Nonlinear Systems. SIAM Journal on Control and Optimization, 2013, 51 (4), pp.3208 - 3234. ⟨10.1137/130908786⟩. ⟨hal-01509334⟩