Fuzzy Gain-Composite approach for robust control of chaotic fractional-order optical systems with guaranteed performance

In this work, a Guaranteed-Cost Fuzzy Gain-Composite (GC-FGC) control scheme was introduced to stabilize a specialized class of chaotic fractional-order Takagi–Sugeno (T–S) fuzzy nonlinear optical systems. The controller design was grounded in fractional-order Lyapunov theory and formulated using Linear Matrix Inequality (LMI) conditions, enabling the effective handling of the complex chaotic dynamics inherent in such systems. The proposed method ensures asymptotic stability and further incorporates a dynamics-free control strategy that remains robust in the presence of system uncertainties and input saturation constraints. To decouple the control rules from the specific system dynamics, the design leverages the norm-bounded nature of the chaotic system states. Furthermore, a deep reinforcement learning framework based on the Soft Actor-Critic (SAC) algorithm was employed to fine-tune the internal coefficients of the GC-FGC controller. By optimizing a reward function through the SAC agent's neural network, an optimal policy was derived that guarantees finite-time convergence and satisfied the sliding surface reachability conditions. The effectiveness and applicability of the proposed control framework were verified through comprehensive simulations and two illustrative numerical case studies.