2019/12/07 by Mohammadreza Doostmohammadian, Doostmohammadian, Mohammadreza, Usman A. Khan +1
Computer Science · Engineering · #Neural Networks Stability and Synchronization #Stability and Control of Uncertain Systems #Distributed Control Multi-Agent Systems
paper · pdf · doi:10.48550/arxiv.1912.03470
In this paper, we consider composite networks formed from the Kronecker\nproduct of smaller networks. We find the observability and controllability\nproperties of the product network from those of its constituent smaller\nnetworks. The overall network is modeled as a Linear-Structure-Invariant (LSI)\ndynamical system where the underlying matrices have a fixed zero/non-zero\nstructure but the non-zero elements are potentially time-varying. This approach\nallows to model the system parameters as free variables whose values may only\nbe known within a certain tolerance. We particularly look for minimal\nsufficient conditions on the observability and controllability of the composite\nnetwork, which have a direct application in distributed estimation and in the\ndesign of networked control systems. The methodology in this paper is based on\nthe structured systems analysis and graph theory, and therefore, the results\nare generic, i.e., they apply to almost all non-zero choices of free\nparameters. We show the controllability/observability results for composite\nproduct networks resulting from full structural-rank systems and self-damped\nnetworks. We provide an illustrative example of estimation based on Kalman\nfiltering over a composite network to verify our results.\n