Non-parametric Model Adaptive Control Based on Gaussian Process Regression

A non-parametric adaptive control algorithm based on Gaussian process regression is proposed for a class of discrete-time nonlinear systems. The pseudo-partial derivative estimation based on Gaussian process regression is devised, and the subset of data approximation is applied to improve this estimation. The estimation of the pseudo-partial derivative and the control law algorithm are combined to give a novel data-driven adaptive control scheme that does not depend on the mathematical model of the controlled system. The monotonic convergence and the BIBO stability of the proposed control algorithm is proved. Simulations indicate the effectiveness and robustness to the models and environments.