A hybrid observer for a distributed linear system with a changing neighbor graph

Abstract

A hybrid observer is described for estimating the state of an m > 0 channel, n-dimensional, continuous-time, linear system of the form x = Ax, y i = C ix , i ∊ {1, 2,…, m}. The system's state x is simultaneously estimated by m agents assuming each agent i senses yi and receives appropriately defined data from each of its current neighbors. Neighbor relations are characterized by a time-varying directed graph N(t) whose vertices correspond to agents and whose arcs depict neighbor relations. Agent i updates its estimate x i of x at “event times” t i , t 2 ,… using a local continuous-time linear observer and a local parameter estimator which for each j ≥ 1, iterates q times during the time interval [tj −1 , tj) to obtain an estimate of x(tj). Subject to the assumptions that none of the C i are zero, the neighbor graph N(t) is strongly connected for all time, and the system whose state is to be estimated is jointly observable, it is shown that for any number λ > 0 it is possible to choose q and the local observer gains so that each estimate x i converges to x as fast as e−λt converges to zero.