Distributed Optimization of Heterogeneous Linear Multi-Agent Systems With Unknown Disturbances and Optimal Gain Tuning

In this paper, we investigate the distributed optimization problem for heterogeneous linear multi-agent systems with unknown disturbances. To solve this problem, we propose a distributed controller design framework, which reduces the controller design for heterogeneous linear multi-agent systems to the stabilizer design for first-order multi-agent systems. By this framework, we propose two kinds of dynamic controllers under the strong convexity of the objective function and the restricted secant inequality condition, respectively. Based on the optimal condition and singular perturbation analysis technique, we prove that the system converges to the optimal state if the disturbances tend to be constant or vary slowly. To further optimize the performance criterion under system stability and input constraint, we provide an optimal gain tuning algorithm such that the system stability, optimality and feasibility are simultaneously achieved. Numerical examples are provided to illustrate the effectiveness of the theoretical results.