On-line Adaptive Interval Type-2 Fuzzy Controller Design via Stable SPSA Learning Mechanism

This paper proposes an interval type-2 Takagi-Sugeno-Kang fuzzy neural system (IT2TFNS) to develop an on-line adaptive controller using stable simultaneous perturbation stochastic approximation (SPSA) algorithm. The proposed IT2TFNS realizes an interval type-2 TSK fuzzy logic system formed by the neural network structure. Differ from the most of interval type-2 fuzzy systems, the type-reduction of the proposed IT2TFNS is embedded in the network by using uncertainty bounds method such that the time-consuming Karnik-Mendel (KM) algorithm is replaced. The proposed stable SPSA algorithm provides the gradient free property and faster convergence. However, the stable SPSA algorithm inherently has the problem for on-line adaptive control. Hence, in order to achieve the on-line result, we utilize the sliding surface to develop a new on-line adaptive control scheme. In addition, the corresponding stable learning is derived by Lyapunov theorem which guarantees the convergence and stability of the closed-loop systems. Simulation and comparison results are shown to demonstrate the performance and effectiveness of our approach.