Recent Developments in Modeling and Analysis of Hybrid Dynamic Systems
Recent research in hybrid dynamic systems has brought together formalisms and techniques from computer science and control theory to address problems involving a mixture of discrete and continuous state variables. Computer scientists have extended standard models of finite-state systems to include continuous dynamics that determine when discrete state transitions can occur. Control theorists have introduced switching logic and discrete states to select continuous dynamic modes in models of controllers and physical systems. The interaction of discrete and continuous phenomena-and the interaction of computer scientists and control theorists-have led to new research problems and new research results. Three models illustrate different perspectives in the hybrid systems literature: block diagrams with discrete and continuous dynamic blocks; hybrid automata with continuous dynamics associated with each discrete state; and continuous Petri nets with continuous dynamics associated with each place. As illustrated by selected examples from the literature, each formalism offers intuitive features for modeling particular classes of hybrid dynamic systems. Computational tools have been developed to model, simulate, and analyze various classes of hybrid systems. To analyze hybrid systems, control theorists have introduced extensions to Lyapunov theory for stability analysis, and computer scientists have extended formal verification techniques to certain classes of hybrid systems. In the latter research, decidability results clearly distinguish tractable from intractable problems. This talk reviews the models, analytical results, and computational tools that have been developed recently for hybrid dynamic systems. The state of the research and prospects for future advances in the theory and applications will be assessed.