An Iterative Method for Control Gain Design of Multiagent Systems With Process Noise

This brief aims to optimize the consensus performance of multiple homogeneous agents, each of which is governed by a general discrete-time linear system with white process noise, exchange state information with its neighboring agents according to an undirected communication topology, and generates its local control in a linear way. The common control gain of agents determines the consensus performance, which is measured by the ultimate mean square deviation of the states of agents. The consensus performance optimization with respect to the control gain takes a nonlinear matrix inequality form and is difficult to solve. To handle this nonlinearity issue, this brief proposes an iterative method. At each iteration, a descent direction of the control gain is computed by solving two linear matrix inequality optimizations based on a given feasible control gain. Then, a line search algorithm is implemented to move the control gain along the obtained descent direction to improve the consensus performance. That updated control gain will work as the starting feasible control gain of the next iteration. This method can well handle the nonlinearity of the original consensus performance optimization and efficiently improve the consensus performance, which is confirmed by simulations.