ADAPTIVE BACKSTEPPING CONTROL OF UNCERTAIN FRACTIONAL ORDER SYSTEMS BY FUZZY APPROXIMATION APPROACH

In this paper, a novel problem of observer-based adaptive fuzzy fractional control for fractional order dynamic systems with commensurate orders is investigated; the control scheme is constructed by using the backstepping and adaptive technique. Dynamic surface control method is used to avoid the problem of “explosion of complexity” which is caused by backstepping design process. Fuzzy logic systems are used to approximate the unknown nonlinear functions. A fractional order Lyapunov function is defined at each stage and the negativity of an overall Lyapunov function is ensured by proper selection of the control law. It is proven that the proposed controller guarantees the boundedness property for all the signals and also the tracking error can converge to a small neighborhood of the origin. Simulation examples are given to demonstrate the effectiveness and robustness of the proposed controllers.