Actuator Selection for Dynamical Networks with Multiplicative Noise

Abstract

We propose a greedy algorithm for actuator selection considering multiplicative noise in the dynamics and actuator architecture of a discrete-time, linear system network model. We show that the resultant architecture achieves mean-square stability with lower control costs and for smaller actuator sets than the deterministic model, even in the case of modeling uncertainties. Networks with multiplicative noise may fail to be mean-square stabilizable by any small actuator set, leading to a failure of a cost-based greedy algorithm. To account for this, we propose a multi-metric greedy algorithm that allows actuator sets to be evaluated effectively even when none of them stabilize the system. We illustrate our results on networks with multiplicative noise in the open-loop dynamics and the actuator inputs, and we analyze control costs for random graphs of different network sizes and generation parameters.