Reachability Analysis Of Nonlinear Hybrid Systems

Hybrid system is a class of complex systems composed of continuous variable dynamical systems and discrete event dynamical systems, which are interacted and influenced with each other. With the development of science and technology, hybrid systems are widely used in the industrial production and social life, and it became the common research focus in computer science and control theory.Reachability of hybrid systems is one of the most basic and important challenging problems in hybrid systems study. The main content of this dissertation focus on reachability of hybrid systems, and the research pivot is focused on reachability analysis of polynomial hybrid systems. The main contributions are as follows.(1)The dissertation use hybrid automatons to discuss the reachability of hybrid systems, and the reachability algorithm of continuous systems and hybrid systems is elaborated. Some tools which can compute approximate reach sets of hybrid systems are introduced, and the method based on the flow pipes is used.(2) To study the problem of reachability of a class of nonlinear hybrid systems, the dissertation presents an verification method based on polyhedron inclusion. Firstly, some notions about linear approximation of nonlinear hybrid systems are introduced. The method based on polyhedron inclusion is proposed to compute the linear approximation of polynomial hybrid systems. And quantifier elimination and nonlinear optimization method are applied to obtain the associated linear hybrid systems. Then the over-approximation of reachable set of original polynomial hybrid systems can be computed by using SpaceEx. Furthermore, the safety properties of the systems also can be verified.(3)A summary of this dissertation is given. And the prospect of the future research is presented.