Modular discrete time approximations of distributed hybrid automata

We consider a network of controllers that observe and control a plant whose dynamics is determined by a finite set of continuous variables. At any given time a variable evolves at a constant rate. However, a controller can switch the rates of a designated subset of the continuous variables. These mode changes are determined by the current values of a designated subset of the variables that the controller can observe. Each variable’s rate is controlled by exactly one controller and its value is observed by at most one controller. We model this setting as a network of hybrid automata and study its discrete time behavior. We show that the set of global control state sequences displayed by the network is regular. More importantly, we show that one can succinctly represent this regular language as a family of communicating finite state automata. We allow the observation of the variables and the changes in the rates of the variables to incur delays. We also permit the digital clocks associated with the controllers to evolve at different–but rationally related–rates.