An Overview of Hybrid Systems Control
John Lygeros · Birkhäuser Boston eBooks · 2005
The term hybrid systems is used in the literature to refer to systems that feature an interaction between diverse types of dynamics. Most heavily studied in recent years are hybrid systems that involve the interaction between continuous dynamics (with a dense state space and evolution determined by differential or difference equations) and discrete dynamics (with a finite or countable state space and evolution according to finite state machines, Petri nets, or other discrete models of computation). The study of this class of systems has to a large extent been motivated by applications to embedded systems and control. Embedded systems by definition involve the interaction of digital devices with a predominantly analog environment. In addition, much of the design complexity of embedded systems comes from the fact that they have to meet specifications such as hard real-time constraints, scheduling constraints, etc. that involve a mixture of discrete and continuous requirements. Therefore, both the model and the specifications of embedded systems can naturally be expressed in the context of hybrid systems. Motivated by the observation that embedded systems often also have to deal with an uncertain and potentially adversarial environment, researchers have in recent years extended their study of hybrid systems beyond continuous and discrete dynamics, to include probabilistic terms. This has led to the more general class of stochastic hybrid systems.