Parameter Optimization of Multi-Agent Formations based on LQR Design

In this paper we study the optimal formation control of multiple agents whose interaction parameters are adjusted upon a cost function consisting of both the control energy and the geometrical performance. By optimizing the interaction parameters and by the linear quadratic regulation(LQR) controllers, the upper bound of the cost function is minimized. For systems with homogeneous agents interconnected over sparse graphs, distributed controllers are proposed that inherit the same underlying graph as the one among agents. For the more general case, a relaxed optimization problem is considered so as to eliminate the nonlinear constraints. Using the subgradient method, interaction parameters among agents are optimized under the constraint of a sparse graph, and the optimum of the cost function is a better result than the one when agents interacted only through the control channel. Numerical examples are provided to validate the effectiveness of the method and to illustrate the geometrical performance of the system.