Individual feedback control scenarios are naturally modeled as interconnections of modules characterized by their input/output behavior. Modal control, by contrast, naturally suggests a state-based view, with states representing control modes. Modern, software-based control systems usually involve both styles of control. The distinct modeling techniques need to be reconciled in order to support a systematic methodology for the design, validation, and implementation of control software.
The dichotomy between the input/output (feedback) view and the state (multi-modal) view is often presented in a restricted setting, as a dichotomy between continuous and discrete control. Continuous feedback control focuses on the analog interaction of the controller with a physical plant, through sensors and actuators. Continuous control models and design techniques have been developed, used, and validated extensively. The case for discrete multi-modal control rests on the observations that discrete abstractions make it easier to manage system complexity, discrete models are easier to manipulate, and discrete representations more naturally accommodate linguistic and qualitative information in controller design. Moreover, every digital (hardware/software) implementation of the controller is ultimately discrete.
The resulting continuous-discrete interplay is often referred to as a hybrid system. Commonly used models for hybrid systems, such as hybrid automata [ACH95], combine state-transition diagrams for discrete behavior with differential equations or inclusions for continuous behavior. Because of the continuous-vs.-discrete focus, however, the mechanisms for composition and abstraction of hybrid automata are rather primitive. These models were developed for studying decision problems about the analysis of hybrid systems, yielding for example conditions under which reachability is decidable. But they have the following shortcomings when used for design: