ON A CLASS OF GENERAL HYBRID DYNAMICAL SYSTEMS

摘要

Complex systems typically possess a hierarchical structure, characterized by continuous-variable dynamics at the lowest level and logical decision-making at the highest. Virtually all control systems today perform computer-coded checks and issue logical as well as continuous-variable control commands. Such are "hybrid" systems. We introduce "gen-eral hybrid dynamical systems" as interacting collections of dynamical systems, evolving on continuous-variable state spaces, and subject to continuous controls and discrete phenomena. We discuss modeling issues, giving conditions for trajectories and providing a taxonomy for hybrid systems models. We review our hybrid systems analysis results, including topology, complexity/computation, stability tools, and examples. We summarize our hybrid control re-sults, including optimal control theory, control algorithms, and examples.