Think globally, communicate, act locally: online parallel/distributed supervisory control

We propose a new algorithm for the online supervisory control of partially observed discrete event systems. This algorithm is a parallel/distributed version of the online algorithm VLP-PO that we proposed in prior work. The situation under consideration in this paper is that of a system whose structure can be expressed as the shuffle of three state machines G₁, G₁₂, and G₂ (with disjoint event sets), where G₁₂ is to be interpreted as a common interface between the two system components G₁ and G ₂. The legal language, denoted K, is global, but it can also be expressed as the parallel composition of two languages, K¹||K², where Kⁱ⊆L(G_i||G₁₂), i=1,2. There are two communicating agents that simultaneously run (online) identical versions of the algorithm but on different models and legal languages: agent i, i=1, 2, operates on subsystem G_i||G₁₂ and legal language Kⁱ. We show that this scheme achieves the same behavior as the sequential VLP-PO algorithm, but at a total execution complexity that is significantly lower; this algorithm generates maximal observable and controllable sublanguages of the given legal language K