Abstract :
A bouncing ball, a network of impulsive biological oscillators, a sampled-data and networked control system, and a supervisory-based feedback control loop are examples of hybrid dynamical systems. These systems contain variables that, in some regions of the state space, change continuously and, in other regions, change instantaneously. Hybrid systems have been studied extensively over the last two decades, with important contributions generated by computer scientists, mathematicians, and control engineers. Interest from the control community is due, primarily, to the recognition that advances in modeling and analysis of hybrid systems may spawn a variety of novel feedback control ideas. This lecture emphasizes a dynamical systems approach to hybrid systems. It describes a modeling framework and a set of structural properties under which the dynamic behavior of a hybrid system is robust. Robustness means that small perturbations to the system lead to correspondingly small changes in the qualitative behavior of the system. This feature is a requirement for feedback control systems of all types, including hybrid control systems. Moreover, the properties that yield robustness also confer to hybrid systems many classical stability analysis tools from continuous-time and discretetime nonlinear systems. These and other hybrid-specific tools serve as the genesis for several hybrid feedback control algorithms. A selection of analysis tools and control algorithms are presented to illustrate recent advances in the field of hybrid systems.
