Distributed Adaptive Control for Uncertain Multiagent Systems with User-Assigned Laplacian Matrix Nullspaces

An important practical problem in the distributed control of multiagent systems is the ability of the closed-loop system to guarantee stability and performance with respect to uncertainties. While there are a wide array of distributed adaptive control architectures that address this problem, they are developed based on a specific Laplacian matrix that has the nullspace generally spanning the vector of ones. The contribution of this paper is to make the first attempt in showing how to design and analyze distributed adaptive control architectures for uncertain multiagent systems with user-assigned Laplacian matrix nullspaces spanning any real vector. For this generalized class of multiagent systems, we first propose a distributed adaptive control architecture to guarantee the closed-loop system stability in the presence of uncertainties. We then utilize the low-frequency learning method in order to address high-frequency oscillations that can result from the fast performance recovery need that requires high-gain learning rates. Illustrative numerical examples are further provided to demonstrate the efficacy of the proposed distributed adaptive control architectures.