Approximate method of distributed control for continuous-time multi-agent systems

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 ARE is the maximal solution of the algebraic Riccati inequality. The algebraic relations of the solutions of the AREs for different weighted matrices are shown and the two distributed controllers are designed: the fully distributed one and the interconnected distributed one. They can give the upper bounds and the lower bounds of the centralized optimal cost function. The distributed optimal closed-loop systems are also asymptotic stable.