Adaptive Dynamic Programming-Based Intelligent Finite-Time Flexible SMC for Stabilizing Fractional-Order Four-Wing Chaotic Systems

Fractional-order four-wing (FO 4-wing) systems are of significant importance due to their complex dynamics and wide-ranging applications in secure communications, encryption, and nonlinear circuit design, making their control and stabilization a critical area of study. In this research, a novel model-free finite-time flexible sliding mode control (FTF-SMC) strategy is developed for the stabilization of a particular category of hyperchaotic FO 4-wing systems, which are subject to unknown uncertainties and input saturation constraints. The proposed approach leverages fractional-order Lyapunov stability theory to design a flexible sliding mode controller capable of effectively addressing the chaotic dynamics of FO 4-wing systems and ensuring finite-time convergence. Initially, a dynamic sliding surface is formulated to accommodate system variations. Following this, a robust model-free control law is designed to counteract uncertainties and input saturation effects. The finite-time stability of both the sliding surface and the control scheme is rigorously proven. The control strategy eliminates the need for explicit system models by exploiting the norm-bounded characteristics of chaotic system states. To optimize the parameters of the model-free FTF-SMC, a deep reinforcement learning framework based on the adaptive dynamic programming (ADP) algorithm is employed. The ADP agent utilizes two neural networks (NNs)—action NN and critic NN—aiming to obtain the optimal policy by maximizing a predefined reward function. This ensures that the sliding motion satisfies the reachability condition within a finite time frame. The effectiveness of the proposed methodology is validated through comprehensive simulations, numerical case studies, and comparative analyses.