Invariant-based Supervisory Control of Switched Discrete Event Systems*

Switched (hybrid) systems have been the subject of numerous studies in modern control theory This paper introduces the notion of switched Discrete Event Systems (s-DES) and investigates its representational and computational potential in (i) the description and the analysis of the emergent behavior, (ii) the specification of the control requirements, and (iii) the eventual computation of the necessary control function. More specifically, it is shown that the potential decomposition of the overall DES behavior in a well defined set of “operational modes” (a) can lead to descriptions of the emergent behavior that reveal important natural attributes of this behavior, and (b) enables the specification of control requirements and the synthesis of the corresponding control laws in a modular and distributed manner that takes full advantage of the aforementioned decomposition. The work is motivated by the need to cope with DES operating under a number of failing modes that result from non-catastrophic failures and repairs, and also DES that might evolve their operation through a number of “stages”.