Study On Robust Adaptive Fuzzy Control Via Backstepping

As one of the major methods of the adaptive control of nonlinear systems, backstepping has been received more and more attention in recent years. In this paper, a class of perturbed strict-feedback nonlinear systems with the form of single-input & single-output (SISO) and multiple-input & multiple-output (MIMO), a class of perturbed pure-feedback nonlinear systems and a class of time-delays nonlinear systems with unknown virtual control coefficients are studied hi turn. Based on the method of backstepping, the design and analysis procedures use a series of control theories such as Lyapunov stability theory, fuzzy approximation theory, adaptive control theory, robust control theory and so on. The main work of this paper is summarized as follows.Firstly, a new design scheme of direct adaptive fuzzy controller for a class of perturbed strict-feedback nonlinear systems is proposed. The design is based on backstepping and the approximation capability of the fuzzy systems with adjustable linear parameters. A continuous robust term is adopted to minify the influence of modeling error or disturbance, and it not only enhances the system's robustness but also improves the flexibility of the design process. Leakage terms are incorporated into the adaptive laws to prevent parameter drifts. The adaptive compensation term of the optimal approximation error is introduced to improve the performance further. By theoretical analysis, the closed-loop control system is proven to be semiglobally uniformly ultimately bounded, with tracking error converging to a residual set.Secondly, above results are extended to MIMO nonlinear systems. The model includes system's external disturbances or unmodeled dynamics. The form of subsystems' high virtual control coefficients is more commonly. Through introducing the modified integral-Lyapunov function, the approach is able to avoid the requirement of the upper bound of the first tune derivation of all the subsystems' high frequency control gains.Thirdly, a new design scheme of direct adaptive fuzzy controller for a class of perturbed pure-feedback nonlinear systems is proposed in this paper. Implicit function theorem and the mean value theorem are exploited to assert the existence of the continuous desired virtual controls. Fuzzy systems with adjustable linear parameters are used to approximate the continuous desired virtual controls and desired practical control.Lastly, adaptive fuzzy control is presented for a class of perturbed strict-feedback nonlinear system with unknown tune delays. By using the property of Nussbaum function, the proposed design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. A continuous robust term is adopted to minify the influence of modeling error or disturbance. The unknown tune delays are compensated for using appropriate Lyapunov- Krasovskii functions in the design.Through the research in this paper, the design and analysis problems for several classes of perturbed nonlinear control systems have been properly solved via the method of backstepping. Numerical simulation experiments of these control schemes demonstrate their effectiveness.