Prescribed performance adaptive fuzzy dynamic surface control of nonaffine time-varying delayed systems with unknown control directions and dead-zone input

In this paper, an adaptive prescribed performance control method is presented for a class of uncertain strict feedback nonaffine nonlinear systems with the coupling effect of time-varying delays, dead-zone input, and unknown control directions. Owing to the universal approximation property, fuzzy logic systems are used to approximate the uncertain terms in the system. Since there is no systematic approach to determine the required upper bounds of errors in control systems, the prior selection of control parameters to have a satisfactory performance is somehow impossible. Therefore, the prescribed performance technique as a solution is applied in this study to bring satisfactory performance indices to the system such as overshoot and steady state performance within a predetermined bound. Dynamic surface control strategy is also introduced to the proposed control scheme to address the "explosion of complexity" behavior existing in conventional backstepping methods. To ease the control design, the mean-value theorem is utilized to transform the nonaffine system into the affine one. Moreover, with the help of this theorem, the unknown dead-zone nonlinearity is separated into the linear and nonlinear disturbance-like bounded term. The proposed method relaxes a prior knowledge of control direction by employing Nussbaum-type functions, and the effect of time-varying delays are compensated by constructing the proper Lyapunov-Krasovskii functions. The proposed controller guarantees that all the closed-loop signals are semiglobally uniformly ultimately bounded and the error evolves within the decaying prescribed bounds. In the end, in order to demonstrate the superiority of this method, simulation examples are given.