Lyapunov-based model predictive control for continuous stirred-tank reactors using physics-informed neural networks and disturbance observer

Abstract

To address modeling complexity and poor control performance of traditional methods for continuous stirred-tank reactors subject to severe nonlinearity, and multivariable coupling, this paper proposes a Lyapunov-based model predictive control strategy integrating physics-informed neural networks and disturbance observers. First, a physics-informed neural network incorporates physical equation residuals into network training, establishing a high-precision discrete data-driven dynamic model without complex mechanistic modeling. Second, to prevent potential divergence of purely data-driven model predictive control in unstable processes, a Lyapunov constraint is incorporated into the optimization scheme to guarantee closed-loop stability. Additionally, a proportional-integral disturbance observer estimates lumped process disturbances online for feedforward and integral compensation. Numerical simulations demonstrate that the physics-informed neural network achieves high prediction accuracy. Under nominal and disturbed conditions, the proposed control strategy achieves rapid and smooth setpoint tracking, eliminates steady-state errors, and demonstrates superior dynamic performance and robustness.