A PINN-Based Safe Model Predictive Control Framework for Nonlinear System with State Constraint

This paper proposes a safe model predictive control (Safe-MPC) framework that integrates physics-informed neural networks (PINNs), model predictive control (MPC), and control barrier functions (CBFs), aiming to achieve safe trajectory tracking of nonlinear systems in complex environments with obstacles. The proposed approach leverages PINNs to learn system dynamics from limited data while preserving physical consistency. The learned model is then embedded into the rolling prediction module of MPC, enabling accurate and real-time solvable control strategies. In parallel, CBFs are incorporated in a soft-constraint formulation to enforce safety constraints on the system states, ensuring that they remain outside unsafe regions throughout the optimization process. Simulation results on a two-dimensional nonlinear system demonstrate that the proposed method can accurately track the reference trajectory and effectively avoid static obstacles. The system trajectory converges stably, validating the effectiveness and safety of the proposed method. Compared with traditional MPC methods based on explicit physical models, the proposed Safe-MPC framework exhibits superior performance in terms of modeling flexibility and tracking accuracy. Future work will extend the framework to higher-dimensional systems and validate its performance on real-world robotic platforms.