Modeling and Analysis of Hybrid Control Systems

We propose a formal approach to the modeling and analysis of hybrid control systems. The approach consists of the interleaved phases of hybrid dynamic system modeling, requirements speciication, hybrid control design and overall behavior veriication. We have developed Constraint Nets as a semantic model for hybrid dynamic systems. Using this model, continuous, discrete and event-driven components of a dynamic system can be represented uniformly. We have developed timed 8-automata as a requirements speciication language for dynamic behaviors. Using this language, many important properties of a dynamic system, such as safety, stability, reachability and real-time response can be formally stated. We have also proposed a veriication method for checking whether a constraint net model satisses a timed 8-automaton speciication. The method uses the induction principle and generalizes both Liapunov stability analysis for dynamic systems and monotonicity of well-foundedness in discrete-event systems. The power of these techniques is demonstrated with a simple elevator system. An elevator system is a typical hybrid system with continuous motion following Newtonian dynamics and discrete event control responding to users' request. We model the complete elevator system using Constraint Nets and verify the overall behavior of the system against the requirements speciication in timed 8-automata.