RBF-ARX model-based trust region nonlinear model predictive control and its application on magnetic levitation ball system

Real-time nonlinear model predictive control (NMPC) of a nonlinear system with extremely short sampling periods poses significant challenges, particularly in balancing optimality in solving non-convex optimization problems with the computational efficiency required for real-time implementation. To address this, a trust region nonlinear model predictive control (TR-NMPC) method is proposed based on a real-time iteration scheme, enabling stable and effective solutions to the non-convex minimization problem inherent in NMPC. Firstly, radial basis function-based autoregressive model with exogenous variables (RBF-ARX) is employed to describe the dynamics of a magnetic levitation ball system, forming the basis in NMPC design. Then, the non-convex optimization problem in NMPC is approximated in the real-time iteration scheme. To constrain the approximation error, we propose and analyze a trust region optimization method, which dynamically adjusts the trust region in each iteration based on the discrepancy between the designed and approximated objective functions. By combining the trust region optimization method with the RBF-ARX model-based parameter scheduling strategy in real-time iteration scheme, the non-convex optimization problem in NMPC is solved with high real-time efficiency. Simulation and real-time control experiments on the magnetic levitation ball system demonstrate that the proposed NMPC method achieves both exceptional computational efficiency and superior transient performance.