On Robust Adaptive Control Via Sliding Mode Control And K-Filter

In the recent years, with the continuous deepening of the control theory study and the need of research and application for a large number of practical systems, such as the power systems, ecological systems, communication systems and industrial engineering systems, etc, the requirement of the performance for control systems becomes higher and higher. The existence of hysteresis, dead-zone and time delay usually causes undesirable inaccuracies, oscillations and even instability for the control systems. Therefore, it has very important theoretical significances and applied value to study the control schemes of the nonlinear systems with unknown nonlinear input and time delay. In this dissertation, based on the principle of sliding mode control and K-filter, several adaptive controllers are designed for nonlinear systems with unknown dead-zone and time delay. The main work of this thesis is outlined as follows.Firstly, based on the principle of sliding mode control, a new scheme of an adaptive fuzzy controller for a class of uncertain SISO nonlinear system with dead-zone nonlinear input is proposed. By use of appropriate integral-type Lyapunov function, the possible controller singularity problem in feedback linearization techniques is avoided. At the same time, two Lyapunov functions are constituted, one determines the bounded region used in modeling, and the other demonstrates that the output tracking error converges to zero. By theoretical analysis, the closed-loop control system is proved to be globally uniformly ultimately bounded (GUUB).Secondly, a new variable structure adaptive control scheme is proposed for a class of uncertain MIMO nonlinear system with dead-zone nonlinear input and time-varying delays. The unknown time-varying delay uncertainties are compensated by use of Lyapunov-Krasovskii functionals in the design. Furthermore, using the Young's inequality and parameter adaptive estimation, the parameters of the nonlinear dead-zone models and lumped uncertainty needn't to be known. By theoretical analysis, the closed-loop control system is proved to be semi-global uniformly ultimately bounded (SGUUB), and the output tracking error converges to a neighborhood of zero.Thirdly, using the approximation capability of the first type fuzzy systems, a robust adaptive output-feedback control scheme is designed for a class of nonlinear systems with unknown dead-zone and high-frequency control gain sign. Combining the Nussbaum gain technique with adaptive backstepping method, the high-frequency control gain sign is assumed to be unknown. By employing the tuning functions, the adaptive law is designed, and the overparametrization is avoided. Furthermore, using the Young's inequality and parameter adaptive estimation, the parameters of the dead-zone model and the upper bound of the disturbances needn't to be known. By theoretical analysis, the closed-loop control system is proved to be semi-global uniformly ultimately bounded (SGUUB).Fourthly, adaptive fuzzy output-feedback control is developed for a class of nonlinear systems with unknown dead-zone and control directions. The design is based on the approximation capability of the first type fuzzy systems. By combining dynamic surface control with output-feedback control, the overparametrization in the output- feedback control design is avoided, without introducing the tuning functions. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system and small tracking error by choosing design constants appropriately.Finally, a robust adaptive output-feedback control scheme based on K-filters is proposed for a class of nonlinear interconnected time-varying delay systems with immeasurable states. It is difficult to design the controller due to existence of the immeasurable states and the time-delay couplings among interconnected subsystems. This difficulty is overcome by use of the approximation capability of the first type fuzzy systems, the backstepping design method, K-filters and appropriate Lyapunov-Krasovskii functionals. Based on Lyapunov theory, the closed-loop control system is proved to be semi-global uniformly ultimately bounded (SGUUB), and the output tracking error converges to a neighborhood of zero.Though the research in this thesis, some robust adaptive control problems for uncertain nonlinear systems with unknown dead-zone and time delay have been properly solved. Numerical simulation experiments of these control schemes demonstrate their effectiveness.