Implicit numerical integration for the simulation and control of a non-smooth system with resets

Abstract

This paper presents a new method for numerical integration of a class of non-smooth systems in the presence of resets in position. The hard non-linearity introduced by resets due to a unilateral constraint on position poses a challenge for traditional numerical integration schemes which invariably result in oscillations. The results of this paper utilize the implicit numerical integration schemes of non-smooth systems to the systems with resets via employing the method of Zhuravlev-Ivanov transformation. The contribution lies in attaining existence of discretization solutions in the presence of the Zeno mode of impacts. We illustrate the effectiveness of the method on regulation and tracking problems. The good results presented here will motivate the theoretical study of those control strategies.