Model Reference Gaussian Process Regression: Data-Driven State Feedback Controller

Abstract: This paper proposes a data-driven state feedback controller that enables reference tracking for nonlinear discrete-time systems. The controller is designed based on the identified inverse model of the system and a given reference model, assuming that the identification of the inverse model is carried out using only the system's state/input measurements. When its results are provided, we present conditions that guarantee a certain level of reference tracking performance, regardless of the identification method employed for the inverse model. Specifically, when Gaussian process regression (GPR) is used as the identification method, we propose sufficient conditions for the required data by applying some lemmas related to identification errors to the aforementioned conditions, ensuring that the Model reference-GPR (MR-GPR) controller can guarantee a certain level of reference tracking performance. Finally, an example is provided to demonstrate the effectiveness of the MR-GPR controller.