Linear quadratic regulator control of multi-agent systems

This paper considers a collection of agents performing a shared task making use of relative information communicated over an information network. The designed suboptimal controllers are state feedback and static output feedback, which are guaranteed to provide a certain level of performance in terms of a linear quadratic regulator (LQR) cost. Because of the convexity of the LQR performance region, the suboptimal LQR control problem with state feedback is reduced to the solution of two inequalities, with the minimum and maximum eigenvalues of the Laplacian matrix as the coefficients. The advantage of the method is that the LQR control problem of network multi‐agent systems can be converted into the LQR control of a set of single‐agent systems, and the structure constraint on the feedback gain matrix can be eliminated. It can be shown that the size of the LQR control problem will not increase according to the number of the node in the fairly general framework. The method can be extended to the synthesis of the static output feedback, which is derived from the weighting matrices in LQR. Through some coordinate transformation and the augmentation of the output matrix, the LQR synthesis is provided on the basis of the output measurements of the adjacent agents. Numerical examples are presented to illustrate the proposed method.