An Estimator-Based Distributed Optimization Algorithm for Affine Formation Control of Second-Order MASs

This paper addresses the optimal affine formation control problem for second-order multi-agent systems (MASs). The control objective is to steer the formation with stress matrix constraints while minimizing the sum of all the local time-varying cost functions. The key challenge is the tight coupling between position tracking, velocity regulation, and time-varying cost minimization. We develop a distributed estimator–controller framework that decouples these dynamics via three local estimators. For each agent, these estimators can track the global optimization variables using only local information from its neighbors. On this basis, a distributed optimizer is designed for the agents. Theoretical analysis shows that, using the proposed optimizer, all agents’ trajectories converge to the optimal solution by a prescribed time, and affine formation is simultaneously achieved within that horizon. Simulation results further illustrate the superior tracking performance of our algorithm in multi-robot scenarios.