Performance analysis of distributed control configurations in LQR multi-agent system design
Ivana Tomić, George D. Halikias · 2016
The paper considers a distributed Linear Quadratic Regulator (LQR) design framework for a network of identical dynamically decoupled multi-agent systems. It is known that in this case a stabilizing distributed controller for the network can be obtained by solving a centralized LQR problem whose size depends on the maximum vertex degree of the graph. A systematic method is presented for computing the performance loss of various distributed control configurations relative to the performance of the centralized controller. A procedure is developed for analyzing the performance loss for general distributed control configurations and state-space directions. It is also shown that by removing a single link we can always define a control configuration for which there is no performance loss, provided the initial state of the aggregate system lies in a particular direction of state-space which is identified. The results are illustrated by an exhaustive analysis of the network consisting of six identical agents.