Distributed Optimization of Heterogeneous Agents by Adaptive Dynamic Programming

In this paper, we study the distributed optimization problem of general linear multi-agent systems with heterogeneous dynamics under directed weight-unbalanced communication topologies. Compared with existing studies, we focus on the case when the dynamics of agents are unknown, which possesses higher application value. To tackle the issues brought by unknown system dynamics, the adaptive dynamic programming method is adopted to design the control law. The feedback gain in the control law and the system dynamics are derived from the input data, the state data, and the output data of the agents. Then, the remaining parameters in the control law are obtained by solving a series of matrix equations based on the identified system dynamics. Based on the certainty equivalence principle, the distributed optimization problem is solved in the sense that the outputs of all agents converge to the optimal solution of the global cost function. Finally, a simulation example concerning a group of resistor-inductor-capacitor (RLC) circuits is presented to verify the effectiveness of the proposed method.