Distributed Optimization-based Formation Tracking for Multi-agent Systems with a Privacy-preserving Mechanism

This paper investigates distributed time-varying optimization-based formation tracking problems for discrete-time heterogeneous multi-agent systems with unknown disturbances. Firstly, an optimization-based formation tracking problem with privacy preservation is established, which formulates the relation between the formation tracking and the distributed optimization on the formation reference. Then, a distributed formation tracking controller composing of differential privacy mechanism and stochastic subgradient method is designed. Furthermore, the privacy, stability and optimality are proved by utilizing the discrete-time Lyapunov method. Finally, numerical simulations demonstrate the effectiveness of the proposed method.