Distributed Optimization for Disturbed Second-Order Multiagent Systems Based on Active Antidisturbance Control.

Abstract

In this article, the distributed optimization problem is studied for second-order multiagent systems with both mismatched and matched disturbances. For this problem, a distributed active antidisturbance control framework is established, which consists of both disturbance estimation/compensation and distributed feedforward-feedback composite control design. In the first stage, some disturbance estimators are utilized to estimate various types of matched/mismatched disturbances for each agent. In the second stage, for each agent, based on the disturbance estimates, the information exchanges between the neighboring agents, and the gradient of the local cost function only accessible to itself, a kind of distributed composite controllers are proposed. Under these controllers, all the agents' outputs asymptotically reach consensus to the minimizer of the global cost function, which is the sum of all the local cost functions. The closed-loop system convergence is proven based on a new Lyapunov function, convex analysis, and an input-to-state stability criterion. Simulations demonstrate the effectiveness of the proposed control scheme.