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

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.