A Nonsmooth Dynamics Perspective on State Observer Design for Mechanical Systems with Unilateral Constraints

Abstract

One of the main difficulties in the state observer design for impulsive mechanical systems is the so-called peaking phenomenon: even for an arbitrarily small pre-impact estimation error, a slight mismatch between the impact time instants of the observer and the observed system can lead to large post-impact estimation error. Therefore, Lyapunov’s stability theorems cannot be directly applied. For linear mechanical systems with unilateral constraints, we propose to take a Nonsmooth Dynamics perspective on the problem, which allows to sidestep the main difficulties by transforming and approximating the original continuous-time system by a discrete linear complementarity system through the use of the Schatzman-Paoli scheme. The discretization acts as a regularization, i.e. the impacts take place over two consecutive time steps. Furthermore, it involves force and impact laws on position-level with the favorable property of maximal monotonicity. Finally, a passivity-based observer design for discrete linear complementarity systems can be applied.