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We consider the problem of coordinating a collection of switched subsystemsunder both local and global constraints for safe operation of the system.Although an invariant set can be leveraged to construct a safety-guaranteedcontroller for this kind of problem, computing an invariant set is not scalableto high-dimensional systems. In this paper, we introduce a strategy to obtainan implicit representation of a controlled invariant set for a collection ofswitched subsystems, and construct a safety-guaranteed controller to coordinatethe subsystems using the representation. Specifically, we incorporate theinvariant set into a model predictive controller to guarantee safety andrecursive feasibility. Since the amount of computations is independent of thenumber of subsystems, this approach scales to large collections of switchedsubsystems. We use our approach to safely control a collection ofthermostatically controlled loads to provide grid balancing services. Theproblem includes constraints on each load's temperature and duration it mustremain in a mode after a switch, and also on aggregate power consumption toensure network safety. Numerical simulations show that the proposed approachoutperforms benchmark strategies in terms of safety and recursive feasibility.

An Invariant Set Construction Method, Applied to Safe Coordination of Thermostatic Loads