Concurrent Learning Based Tracking Control of Nonlinear Systems using Gaussian Process

This paper demonstrates the applicability of the combination of concurrent learning as a tool for parameter estimation and non-parametric Gaussian Process for online disturbance learning. A control law is developed by using both techniques sequentially in the context of feedback linearization. The concurrent learning algorithm estimates the system parameters of structured uncertainty without requiring persistent excitation, which are used in the design of the feedback linearization law. Then, a non-parametric Gaussian Process learns unstructured uncertainty. The closed-loop system stability for the nth-order system is proven using the Lyapunov stability theorem. The simulation results show that the tracking error is minimized (i) when true values of model parameters have not been provided, (ii) in the presence of disturbances introduced once the parameters have converged to their true values and (iii) when system parameters have not converged to their true values in the presence of disturbances.