Closed Form Solutions of Hybrid Systems

Dr. Martin v. Mohrenschildt


In this paper we present a new symbolic approach to hybrid systems. Hybrid systems are systems containing both, continuous and discrete changing quantities. We model hybrid systems using hybrid automata: Hybrid automata extend the classical notion of finite state machines by combining differential equations to model the dynamic behavior of systems with a finite control. In contrast to other approaches we consider a hybrid automata as a generalization of differential equations and develop the notion of a symbolic ``closed form" solution of a hybrid automata. A closed form solution is an expression which gives the value of the quantities in question as a function of design parameters and time. These solutions allow us to perform the verification of design properties. We were able to detect design constrains on control systems that other methods fail to detect. This paper gives the basic definitions, algorithms, and an example to demonstrate the advantage of the proposed approach.