Cooperative Control of Uncertain Multiagent Systems via Distributed Gaussian Processes

For single agent systems, probabilistic machine learning techniques such as Gaussian process regression have been shown to be suitable methods for inferring models of unknown nonlinearities, which can be employed to improve the performance of control laws. While this approach can be extended to the cooperative control of multiagent systems, it leads to a decentralized learning of the unknown nonlinearity, i.e., each agent independently infers a model. However, decentralized learning can potentially lead to poor control performance, since the models of individual agents are often accurate in merely a small region of the state space. In order to overcome this issue, we propose a novel method for the distributed aggregation of Gaussian process models, and extend probabilistic error bounds for Gaussian process regression to the proposed approach. Based on this distributed learning method, we develop a cooperative tracking control law for leader-follower consensus of multiagent systems with partially unknown, higher order, control-affine dynamics, and analyze its stability using the Lyapunov theory. The effectiveness of the proposed methods is demonstrated in numerical evaluations.