Model-free Output Consensus Control for Nonlinear Multi-agent Systems with Random Disturbance

The model-free output consensus control problem for the nonlinear multi-agent systems (MASs) with random disturbance is considered. In order to avoid the difficulty of designing a consensus protocol when the dynamic model is unknown, this paper proposes an online learning method for a consensus protocol by Gaussian regression based two-phase iteration. First, output of the leader is estimated by an adaptive distributed observer. On this basis, measurable input/output data is used to solve the consensus control problem of model-free systems. A two-phase iteration for Gaussian-kernel based adaptive critic design (GK-ACD) is proposed to approximate optimal Q-function and optimal control policies, which can simultaneously approximate and update value functions and hyper-parameters. This avoids the problem of artificial selection of improper hyper-parameters may mislead the kernel-based regression. Finally, the simulation results show that, without knowledge of dynamics, the distributed policies achieves the output consensus control of nonlinear MASs, and proves the effectiveness of the method.