Adaptive T–S fuzzy control design for fractional-order systems with parametric uncertainty and input constraint

Abstract

Thanks to the superiority of fractional differential equations in modeling high technology dynamical real world systems, the design and control of fractional-order systems have been widely investigated in recent decades. On the other hand, supposing that dynamic equations of the fractional-order systems usually include various parameters and nonlinear terms, Takagi–Sugeno (T–S) fuzzy models with if–then rules can used to characterize the systems' dynamics. Also, the control community knows that there are usually some nonlinearities, such as dead-zone, backlash, hysteresis and saturation, in control actuators which can decrease the ideal prescribed performance of the fractional systems. The saturation nonlinearity is perhaps the most commonly existed one in control applications of fractional nonlinear systems that should be compensated by a proper method. So, this article proposes a novel adaptive T–S fuzzy variable structure control technique for nonlinear fractional-order systems in spite of the saturating input and control fluctuations. The parameters of the fractional system as well as those of the saturation function are presumed to be unknown. Accordingly, update rules are extracted to estimate such fluctuations. Then, simple adaptive linear-like control rules are developed according to the T–S fuzzy control theory. The stability of the origin equilibrium point of the final closed-loop system is assured by Lyapunov stability theory. At last, comparative computer simulations are presented to highlight the accuracy and applicability of the proposed adaptive fuzzy saturated control methodology.