Distributed Identification With Input Design for Network Systems

The distributed identification of network systems under local observation has recently become one of the research hot spots. Due to the unobservable influence of other subsystems and the noise, it is difficult for local subsystems to achieve convergent identification under local observations. This article proposes a distributed identification algorithm for local subsystems to identify their parameter matrices under local observation with a guarantee of convergence. We obtain the necessary and sufficient conditions for the convergence of local identification. We prove that by injecting an independent random signal to the local subsystem, which is easy to implement, using a simple least-squares method to identify local systems can achieve convergent identification for a certain probability. Meanwhile, we give the minimal level of variance of the injected signal that can still guarantee the convergence of the identification. Next, we add the designed input as a vector of Gaussian noises with decreasing variance to a known controller, proving that it can converge to the original controller. Simulations demonstrate the effectiveness of the proposed algorithms.