Adaptive Gain Observers for Distributed State Estimation of Linear Systems

In this paper, we present an adaptive gain distributed state estimation scheme for reconstructing the states of a linear time-invariant (LTI) system by using multiple sensing agents that communicate with each other. To this end, we design observers at each agent with adaptive gains, which uses the (local) partial output measurements and data from neighboring agents to estimate the overall state information. Moreover, to ensure stable online adaptation, we introduce an auxiliary error system at each observer to tune the observer gains. We then employ the Lyapunov stability theory to guarantee the asymptotic convergence of the observer state estimation error, auxiliary error system states, and gain estimation errors when the communication topology is modeled by an undirected, strongly connected graph. Furthermore, we investigate large-scale interconnected systems with strong physical coupling dynamics and extend the proposed analytical design of the state estimation scheme. Finally, we validate the analytical design using the simulation analysis.