Dynamic Surface Fuzzy Control For A Class Of Uncertain Nonlinear Time - Delay Systems

Compared with Backstepping, dynamic surface control is superior to it in terms of computing and it has become a novel method for researching the stability of nonlinear systems recently. The dynamic surface control can avoid the “explosion of terms” which occurs in the backstepping, so it has been widely used in the filed of nonlinear systems. For the unknown functions in the uncertain system, using the fuzzy logic system approximating the unknown functions in the whole systems can solve the controller design problems and it can also adjust the unknown parameters to reach the stability. This paper based on dynamic surface control and adaptive fuzzy control, studies the controller design problems of uncertain nonlinear systems. It mainly involves several aspects: nonlinear time-delay systems, dynamic surface control, fuzzy control, and Lyapunov stability. The main contributions of this paper are outlined as follows:Firstly, fuzzy logic control is used to approximate the unknown functions of state-measurable nonlinear constant time-delay systems. By combining with the approach of dynamic surface control, we put forward a scheme for adaptive fuzzy dynamic surface control.In this scheme, the common assumptions on the delays are removed; the structured Lyapunov–Krasovskii function eliminates the delays’ influence on stability of the closed loop system, it can also guarantee stability of the system. All the signals in the closed-loop system are proved semi-globally uniformly ultimately bounded, and the tracking error can converges to a small neighborhood of the origin.Secondly, focusing on a class of state-unmeasurable nonlinear constant time-delay systems, we use the adaptive fuzzy dynamic surface control in the same way. This approach avoids tedious derivation of virtual controllers in backstepping,thus it simplifies the design steps. For the limitations of state-unmeasurable, in this paper, we have designed state observer, constructed Lyapunov function. It has guaranteed system’s stability and the output can converge to a small neighborhood of the desired reference signal.The controller design and stability analysis of a class of uncertain state-measurable and state-unmeasurable nonlinear time-delay system have been studied in this paper. Through simulation examples, the feasibility of the proposedapproach is proved.