The application of trajectory-based analysis for hybrid systems

Abstract

This thesis is about a trajectory-based approach to analysis of hybrid system models. In particular, we are interested in analyzing whether a specified set of states can be reached or avoided by all the trajectories within certain time horizon. This is called the reachability and safety verification problem. In addition, given that some trajectories violate the desired properties (for example, they have reached an undesired state), we are interested in whether these faulty trajectories can be diagnosed in time. This problem is referred to as fault diagnosability analysis.

Finally, we present implementation of the approach as a MATLAB toolbox STRONG. The tool supports numerical simulation of hybrid system models, computation of (enlarged) robust neighborhoods, and parallelization of the procedure.

Based on the (enlarged) robust neighborhoods computed from the finitely many simulations, we propose two ways of analyzing fault diagnosability of the hybrid system. One is by state estimation: We construct a discrete and continuous state observer that also serves as a fault diagnoser, and indicates fault diagnosability. In the second way, we use a special metric in the (enlarged) robust neighborhood computation. As results, we prove a quantitative relation between fault diagnosability of the infinitely many trajectories of the system and the finitely many trajectories simulated, and deduce the former from the latter. We extend the results to hybrid system models with probabilistic reset.

We first introduce the enlarged neighborhood approach, which is an extension to the existing robust test generation and coverage method. Using the approach, reachability and safety properties of infinitely many trajectories can be mathematically proved by finitely many simulations.

Our research focuses on formally proving reachability, safety and diagnosability properties for hybrid systems using simulation-based method. The approach applies to hybrid system models with infinite many initial states and non-deterministic events. It maintains feasibility to high-dimensional systems, and is suitable for computer-aided numerical implementation.