Data-driven parallel linear controllers for reference tracking in nonlinear systems

Reference tracking control for nonlinear systems presents significant challenges, particularly when system models are unavailable and real-time computation is required. We present a purely data-driven approach for reference tracking control, referred to as parallel linear controllers (PLIC), which leverages an architecture composed of two linear controllers operating concurrently in distinct dimensional spaces. These controllers are employed for inverse control and mismatch error compensation, respectively. The first controller utilizes the Koopman operator for lifting the system to a high dimension and solves a quadratic program that facilitates constraint handling. The second controller, which works in the original state space, employs the direct data-driven virtual reference tuning approach with some appropriate modifications. The closed-loop properties of the proposed PLIC are analyzed, and the efficacy of the proposed method is exemplified through benchmark simulation.