Control-Invariance of Sampled-Data Hybrid Systems with Periodically Clocked Events and Jitter

Abstract

A hybrid automaton is widely used as a model of hybrid systems. A computer-controlled system is an example of hybrid systems since it has both continuous and discrete variables associated with the physical process (the plant) and the logical dynamics (the control logic and external environment), respectively. In the computer-controlled systems, the measurements and subsequent discrete control actions are usually time-driven events and there exist the jitter variations in their occurrence times. Silva and Krogh proposed an extension of a hybrid automaton called a sampled-data hybrid automaton (SDHA) to model explicitly discrete transitions that are based on time-driven sampling of the continuous state and define a transition system called a sampled-trace transition system (STTS) as semantics to verify its dynamics. The SDHA is a pair of a clock structure and a hybrid automaton with clocked and unclocked events. Unclocked events are enabled when its continuous states satisfy their guards while clocked events are time-driven, that is, they are enabled only at specified sampling times in addition to constraints for their guards. A clock structure, which is given by variation interval in the initial phase, a period of clocked times, and a sampling jitter, specifies sequences of sampling times that can be generated in the system.