Hybrid Systems: Deterministic to Stochastic Perspectives

Abstract

This chapter constitutes a smooth introduction in the field of hybrid systems, discussing issues like modelling classes, analysis and verification, how randomness appears and which stochastic models can be used to capture it. The chapter starts with the presentation of models for deterministic hybrid systems considering two main approaches: the automata perspective and the dynamical system perspective. Then existing algorithmic (model checking) and deductive (theorem proving) techniques for hybrid systems are briefly discussed. The main body of this chapter is dedicated to the description of stochastic models that result by randomising different elements in the structure of classical hybrid systems. Classes of stochastic hybrid systems (like probabilistic hybrid automata, stochastic hybrid automata, switching diffusion processes, general stochastic hybrid automata) are briefly exposed and comparison criteria are underlined.