Supervisory hybrid systems

Supervisory hybrid systems are systems generating a mixture of continuous-valued and discrete-valued signals. This systems paradigm is particularly useful in modeling applications where high-level decision making is used to supervise process behavior. Hybrid system methodologies are also applicable to switched systems where the system switches between various setpoints or operational modes to extend its effective operating range. Hybrid systems, therefore, embrace a diverse set of applications. There has been considerable activity in the area of hybrid systems theory, and this article provides an introduction to some of the basic concepts and trends in this emergent field. The term hybrid refers to a mixing of two fundamentally different types of objects or methods. The paper deals with supervisory hybrid systems. Supervisory hybrid systems are systems that combine discrete event and continuous-valued dynamics. The article is organized as follows. We first provide an example of a hybrid system, to be used throughout as a pedagogical tool illustrating various concepts in hybrid systems theory. We then discuss modeling frameworks for hybrid systems, paying specific attention to the hybrid automaton. Not only may the system have a hybrid character, but the specifications on desired system behaviors may also be hybrid. The article also discusses specification logics that express system requirements on both the discrete and continuous states of the system. The article continues with a survey of current methods and concepts used to verify or validate desired system behaviors, and concludes with a survey of current methods for hybrid control system synthesis.