Model predictive control (MPC) is an effective strategy for regulating constrained nonlinear systems, but its real-time implementation becomes challenging for high-order models and under uncertainty due to the need for repeated online optimization. Learning-based surrogates can alleviate this computational burden by approximating MPC policies. However, most existing approaches are trained under nominal conditions and exhibit limited robustness to disturbances, actuator faults, and distribution shifts. This paper proposes a disturbance-conditioned LSTM–MPC control framework that integrates a pre-trained long short-term memory (LSTM) network, a finitetime disturbance observer, and a Lyapunov-based robust correction mechanism. The LSTM is trained offline using disturbance-informed data to approximate the optimal nonlinear MPC policy, enabling it to learn how control actions vary under different disturbance conditions. During online operation, a disturbance observer reconstructs the combined effects of actuator faults, saturation, and modeling uncertainties in finite time, and these estimates are used to adapt the predictive control policy without repeated optimization. A robust correction term is incorporated to compensate for neural approximation errors and transient estimation inaccuracies, ensuring stable closed-loop performance under bounded disturbances. The framework is evaluated on a nonlinear nanobeam system governed by nonlocal strain-gradient elasticity, representing size-dependent systems with strong nonlinear dynamics. Numerical results under unseen initial conditions, actuator saturation, and time-varying faults demonstrate that the proposed controller achieves tracking performance comparable to or better than nonlinear MPC while reducing online computation time by approximately three to four times. These results show that explicit disturbance conditioning significantly enhances the robustness and generalization of learning-based MPC surrogates, making the proposed approach well suited for real-time control of nonlinear systems under uncertainty
Alsaadi et al. (Fri,) studied this question.