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
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.
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