Distributed Optimal Consensus Control of Multiagent Systems Involving State and Control Dependent Multiplicative Noise

This article aims to solve the multiobjective optimization control problem by investigating the consensus problem of multiagent simultaneous optimization with state and control dependent multiplicative noise. The main contributions of this work are two-fold. First, the optimal consensus control problem is solved by designing the free item of an optimal controller, and the coefficient of the feedback gain is obtained based on analyzing a parameterized generalized algebraic Riccati equation. Second, we derive a new consensus controller that comprises two parts different from the current consensus. One part minimizes a linear quadratic index with a singular control weighting matrix, and the other affords the multiagent systems to achieve mean square consensus.