Continuous Distributed Robust Optimization of Multiagent Systems With Time-Varying Cost

This paper investigates a robust distributed optimization problem for multi-agent systems with time-varying cost subject to disturbances. For first-order and second-order systems with bounded disturbances, an integral sliding mode control framework minimizing the global cost function is presented. For the case with derivative-bounded disturbances, a terminal sliding mode based controller comprising a reference model and a tracking controller is proposed. The reference model based on a nominal distributed optimization algorithm plays the role of generating the optimal signal, while the tracking controller is responsible for tracking the optimal signal despite the disturbances. Convergence of the proposed algorithms is proved strictly by means of Lyapunov analysis and homogeneity techniques. The obtained results are also extended to high order integral chain dynamics. The effectiveness of the methods is illustrated by numerical simulations.