Optimal design of adaptive interval type-2 fuzzy sliding mode control using Genetic algorithm

In this paper, a stable indirect adaptive interval type-2 fuzzy sliding mode control (AIT2-FSMC) is introduced for a class of nonlinear systems. In the presence of uncertainties, especially under noisy and external disturbances, interval type-2 fuzzy system can be helpful in approximating unknown nonlinear system functions. To achieve more efficiency, the proposed controller is designed to use the targeted combination of sliding mode as a robust controller, interval type-2 fuzzy system as a universal approximator, and adaptive control law as an online parameter´s tuner. The interval type-2 adaptation law is derived using Lyapunov approach, and mathematical analysis proves the closed loop system to be asymptotically stable. Although stability of the controller is provided via Lyapunov approach, optimization is required for performance improvement. Genetic algorithm (GA), as a population-based approach, is then used to optimize the parameters of the interval Type-2 fuzzy sets. Simulation analysis shows that the optimized IT2FSMC can reach improved performance.