Study On Adaptive Fuzzy Control Based On Small Gain Theorem

Adaptive control of nonlinear systems is an important topic in control theory at present which can find broad applications. And the study of adaptive control problems in nonlinear systems has great academic value and significant applications. In terms of input-to-state stability (ISS) and small gain theorem, and combined backstepping and dynamic surface control technique, several adaptive control design and analysis methods are presented in this thesis. The main contributions are as follows.Firstly, a design scheme of robust adaptive fuzzy controller is proposed for a class of SISO nonlinear systems with unknown dead-zone. Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertain system function. The approach doesn't require a priori knowledge of the upper bound of dead-zone model parameters and the derivative of control gain function. Furthermore, only one uncertain function is approximated by T-S fuzzy systems and only one learning parameter needs to be adjusted on line. The resulting closed-loop system is proven to be semi-globally uniformly ultimately bounded and the output tracking error converges to a neighborhood of zero.Secondly, based on input-to-state stability (ISS) and small gain theorem, an adaptive fuzzy control scheme is proposed for a class of uncertain strict-feedback nonlinear systems by use of backstepping method. The approach removes the condition of the derivative of virtual control gain functions and reduces the number of adjustable parameters. By theoretical analysis, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded, and the output tracking error converges to a neighborhood of zero by choosing appropriate parameters.Thirdly, an adaptive fuzzy control scheme is proposed for a class of strict-feedback nonlinear systems with unknown dead-zone. By using dynamic surface control and introducing first order filter, the explosion of complexity caused by repeated differentiations of virtual control in traditional backstepping design is eliminated. By constructing of two interconnected subsystems satisfying ISS condition, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded using small gain theorem.Fourthly, by use of mean value theorem and backstepping technique, a robust adaptive fuzzy control scheme is proposed for a class of nonlinear systems in pure feedback form via input-to-state stability (ISS). Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertain nonlinear functions and lower learning parameters need to be adjusted on line. Based on small gain theorem, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded, and the tracking error converges to a neighborhood of zero by choosing appropriate parameters. Lastly, an adaptive fuzzy control scheme based on input-to-state stability (ISS) and small gain theorem is proposed for a class of nonlinear systems in pure feedback form with unknown dead-zone by using dynamic surface control and the approximation of Takagi-Sugeno type fuzzy logic systems. The number of adjustable parameters is reduced effectively by the approach. And the explosion of complexity in traditional backstepping design caused by repeated differentiations of virtual control is avoided. By constructing of two interconnected subsystems satisfying ISS condition, the closed loop control system is proven to be semi-globally uniformly ultimately bounded using small gain theorem.Through the research in this thesis, several adaptive control problems of uncertain nonlinear systems have been properly solved. Numerical simulation experiments of these control schemes demonstrate their effectiveness.