State estimation for a class of nonlinear switched systems using Petri Net

In this paper, we focus on the synthesis of a hybrid observer for a class of nonlinear switched systems where the evolution of the discrete state is governed by a Petri Net. The switched systems, herein, considered are characterized by switching laws that can depend on both the continuous states and external events. A new observer composed of a continuous and a discrete observer in interaction is designed. The continuous observer is based on the second order sliding mode approach to reconstruct the continuous state without using any information about the discrete state after the transformation of the original system in a canonical form. From these estimated continuous states, some discrete modes are determined thanks to the depending of states switching laws. The discrete modes depending on external events cannot be estimated from the knowledge of the continuous states. The estimated modes from the continuous states are considered as observables modes by the discrete observer in order to give the complete discrete states estimation. An illustrative example ends the paper and shows the efficiency of the proposed approach.