Output Tracking Control of Nonlinear Systems With Statistical Learning-based Extremum Seeking

In this paper, we propose a closed-loop output tracking and optimization framework based on active disturbance rejection control (ADRC) and statistical learning for a class of multi-input multi-output (MIMO) systems with stochastic disturbances. We consider the output of an MIMO system associated with an unknown performance function, and a Gaussian kernel-based learning approach is employed to learn the performance function and provides the gradient estimation. The setpoint of the controller is provided by the learning procedure and an ADRC controller is designed to drive the system output to the desired setpoint. Additionally, the practical convergence of the ADRC is proved and the boundedness of the error between the optimal point obtained using the learned model and the actual optimal point is established. Finally, we demonstrate the effectiveness of the proposed algorithm through a numerical example.