Adaptive Control of Nonlinear Systems: Parametric and Non-Parametric Approach

Adaptive control of nonlinear systems is a well-established domain due to its ability to accommodate dynamic variations and uncertainty. However, one of the primary challenges in adaptive control of linearizable structures is identifying the feedback control law's coefficients. Therefore, a complete framework to determine the linearizing control is proposed without any assumptions or prior knowledge of the system parameters using the Dynamic Regression Extension and Mixing (DREM). Parameters are estimated and updated online to ensure the exact cancellation of nonlinear terms required by the linearization process. The proposed method exhibits the global convergence of coefficients and improved transient response. Moreover, a comparison study between parametric and non-parametric approaches is also presented in this paper. Different white-box and black-box methods, namely Artificial Neural Network (ANN), Gaussian Process (GP), Concurrent Learning (CL), and DREM, are applied to estimate the parameter for linearizing control under uncertainties, and their results are compared. The effectiveness of the proposed methodology has been validated on an inverted pendulum using MATLAB and Simulink.