Distributed Optimization of Heterogeneous Linear Multi-Agent Systems with Unknown Disturbances
Mengmeng Duan, Shanying Zhu, Ziwen Yang, Cailian Chen, Guan Xinping · 2024
In this paper, we investigate the distributed optimization problem for heterogeneous linear multi-agent systems with unknown disturbances. By applying the primal-dual method and the time-scale separation technique, a distributed dynamic controller without using any disturbance information is proposed. Based on the optimal condition, the relationship between the optimal solution and the equilibrium point of the system is established, and it is shown that the distributed optimization problem is solved provided that the closed-loop system is stable. Then, inspired by the nonsingular perturbation analysis, it is proved that the closed-loop system is exponentially input-to-state stable with respect to the derivative of the disturbance. Numerical examples are provided to illustrate the theoretical results.