Robust stabilization of fractional-order hybrid optical system using a single-input TS-fuzzy sliding mode control strategy with input nonlinearities

Hybrid optical systems with integrated control mechanisms enable a dynamic adjustment of optical components, ensuring real-time optimization, adaptability to changing conditions, and precise functionality. This control requirement enhances their performance in applications demanding responsiveness, such as autonomous systems, adaptive optics, and advanced imaging technologies. This research introduces a novel approach, employing a dynamic-free Takagi-Sugeno fuzzy sliding mode control (TS-fuzzy SMC) technique, to regulate and stabilize a specific category of chaotic fractional-order modified hybrid optical systems. The method addresses uncertainties and input-saturation challenges within the system. Leveraging a novel fractional calculus definition along with the non-integer type of the Lyapunov stability theorem and linear matrix inequality principle, the TS-fuzzy SMC approach was applied to effectively mitigate and regulate the undesired behavior of the fractional-order chaotic-modified hybrid optical system. Notably, this scheme achieved control without experiencing undesirable chattering phenomena. The paper concludes by offering concrete examples and comparisons, demonstrating how the theoretical findings are applied in real-world scenarios. This provides practical insights into the effectiveness of the proposed approach in diverse applications.