An Explicit Model Predictive Control Framework Based on Physics-Informed Neural Networks

This paper presents a novel control framework that integrates Physics-Informed Neural Networks (PINNs) with Model Predictive Control (MPC) for nonlinear dynamical systems. Unlike traditional MPC, which requires solving optimization problems in real time, the proposed method trains a single feedforward neural network to serve as an explicit controller that directly maps the current state, set-point, and disturbance signals to optimal control actions. The network is trained using a composite loss function that enforces the governing differential equations while incorporating control-oriented objectives such as set-point tracking, control smoothness, and soft constraints on states, inputs, and outputs. The proposed controller is validated on both single-input single-output (SISO) and multi-input multi-output (MIMO) water-tank benchmark systems, demonstrating accurate set-point tracking, effective measured disturbance rejection, and strong generalization across thousands of randomized test scenarios. A runtime comparison with a nonlinear MPC performing online optimization confirms that the explicit PINN-MPC approach achieves comparable control performance while requiring several orders of magnitude less computation time. These results highlight the scalability and computational efficiency of the proposed framework, positioning it as a novel paradigm for real-time control of nonlinear systems.