Supervisory Hybrid Control Systems
2009
The exploitation of well-honed techniques and the exploration of new challenges need not be mutually exclusive strategies for research. This maxim is illustrated by an emerging technology in control: hybrid dynamical systems. These systems combine, within a unified framework and formulation, discrete-event systems (for more on these systems, see Chapter 2) and continuous-time dynamics. Hybrid systems represent a broadening of the scope of control, with infusions of ideas and theories from other fields, especially formal methods in computer science. This chapter discusses hybrid systems in some depth, with particular emphasis on supervisory applications. In this case, the discrete events are viewed as supervisory decisions affecting the qualitative behavior of a system, with different ?>modes ?> of behavior exhibiting different continuous dynamics. An example of a two-arm robotic platform is used to motivate the technical discussion, and other applications are also noted. Other chapters in this volume also outline applications of hybrid dynamical systems (e.g., Chapter 14). Variable structure control, the topic of Chapter 8, can also be considered a hybrid system approach to control. This chapter introduces and explains several new concepts, borrowed in some cases from computer science, that are important for the analysis and synthesis of supervisory hybrid systems. Hybrid automata, an extension of finite state machines, are a popular representational formalism. Together with temporal logics, which can be used to formulate specifications for hybrid control systems, these representations allow the safety and performance of the system to be automatically determined, under some assumptions.