On the control of finite-dimensional mechanical systems with unilateral constraints

This paper focuses on the problem of the control of a class of mechanical systems with a finite number of degrees-of-freedom, subject to unilateral constraints on the position. Roughly speaking, those systems are described by a set of ordinary differential equations that represent smooth dynamics, together with an algebraic inequality condition F(q)⩾0 (where q is the vector of generalized coordinates) and an impact rule relating the interaction impulse and the velocity. Nonsmooth dynamics is at the core of the study of such systems. This implies that one can suitably define solutions and stability concepts that fit with the considered model. We then discuss the closed-loop control problem, and analyze various switching control strategies