Data-Driven Learning Distributed Optimization of Heterogeneous Linear Multiagent Systems

In this article, we investigate the distributed optimization problem of heterogeneous general linear multiagent systems by the adaptive dynamic programming (ADP) approach over directed communication networks. A distinctive feature of this work is the development of a data-driven approach that eliminates the need for prior knowledge of system dynamics for all agents. To address the challenges posed by unknown system dynamics, we utilize the ADP-based data-driven approach to develop the distributed optimization control law. First, the feedback gain of the control law is determined based on the state and input data of the controlled systems. Next, the system dynamics are reconstructed using the solved feedback gain and the running data of the controlled systems. Then, the remaining parameters in the control law are designed by solving a series of steady-state equations. Under standard assumptions and through the application of the certainty equivalence principle, we prove that the proposed approach solves the distributed optimization problem, ensuring output consensus of all agents at the optimal solution of the global cost function. Finally, the viability of our proposed approach is demonstrated through its application to optimal output power sharing control of hydraulic turbine systems and their large-scale form.