Minimal sensor activation for co-detectability of multi-agent discrete event systems

In this paper, we consider a minimal sensor activation problem for co-detectability of multi-agent discrete event systems. Multiple agents are used to observe (and control) a discrete event system. Each agent can observe a subset of events corresponding to its local sensors. The goal of the agents is to estimate and determine the state of the system. This state estimation problem has been studied previously. The main difference between this paper and previous papers is that in this paper, we assume that the sensors are not always activated. They are activated by the agents whenever necessary in order to ensure co-detectability, that is, to ensure at least one agent knows the state of the system. To properly activate sensors, we show that the sensor activation policies must be feasible. If a sensor activation policy is not feasible, we show that we can always construct its maximal sub-policy that is feasible. Under this feasibility condition, co-detectability can be checked by constructing a special co-observer. We show how to construct such a co-observer. Our objective is to minimize sensor activation. This means activating as little sensors as possible and as little time as possible, without violating co-detectability. Algorithms are developed in the paper to obtain minimal sensor activation policies.