On robust and optimal imperfect information state equipartitioning for network systems

Abstract

This paper addresses some fundamental questions towards robust and optimal imperfect information state equipartitioning by means of a computational framework of a system-theoretic approach called semistable Gaussian Linear-Quadratic Consensus (LQC), which is motivated by Optimal Semistable Control (OSC). OSC deals with an optimal regulation problem for dynamical systems with unknown, nonzero set-points. In this paper, we address stochastic OSC for robust and optimal information state equipartitioning under Gaussian white noise disturbance or measurement and random distribution of initial conditions. We develop a new framework for semistable Gaussian LQC and recast the proposed problem into an alternative, constrained optimization problem. To this end, necessary and sufficient conditions to connect semistability and optimal information state equipartitioning are derived in the paper and the existence of optimal solutions to this optimization problem has been proved for network systems. To efficiently solve the proposed constrained optimization problem, we propose a convergence guaranteed numerical algorithm. The rigorous convergence proof of this algorithm is presented and simulation results show the efficacy of the proposed approach.