Model Reference Gaussian Process Regression: Data-Driven State Feedback Controller for Strongly Controllable Systems

Data-driven control methods are gaining importance in control engineering, particularly for nonlinear systems where traditional models fall short. Many approaches rely on predefined libraries of functions, such as polynomials, to approximate system dynamics. These methods assume the selected functions can effectively represent the underlying system, but this assumption may not always hold, potentially impacting the robustness of control designs. The Model Reference Gaussian Process Regression (MR-GPR) controller was introduced to address these issues by using Gaussian Process Regression (GPR) with flexible kernels that adapt to observed data, eliminating the need for predefined function libraries. In this paper, we extend the MR-GPR controller to handle n-step controllable systems, allowing for more complex multi-step control tasks. We propose a state feedback control strategy based on realtime system data. Theoretical analysis confirms the stability of the closed-loop system under the MR-GPR controller, and numerical simulations validate its effectiveness.