A new approach to distributed control for multi-agent systems based on approximate upper and lower bounds

In this paper, the distributed control of the LQR problem for continuous-time multi-agent systems is considered. Based on the centralized optimal control, we prove that the solution of the algebraic Riccati equation is the maximal solution of the algebraic Riccati inequality. The algebraic relations of the solutions of the algebraic Riccati equations for different weighted matrices are shown and two distributed controllers are designed: the fully distributed one and the interconnected distributed one. They can provide an upper bounds and a lower bounds of the centralized optimal cost function. The optimal closed-loop feedback control systems for the two distributed controllers are also asymptotically stable. Some examples are given to show the correctness of the proposed results.