Study On Robust Adaptive Fuzzy Control With Unknown Control Gain Sign

In recent years, fuzzy modeling based robust adaptive control for nonlinear systems has been a hot topic in the field of intelligent control. Some correlative problems in this area are studied in this paper.Firstly, two design scheme of direct adaptive fuzzy controller for a class of uncertain nonlinear systems with unknown control gain sign are proposed. The design is based on the principle of sliding mode control and the approximation capability of fuzzy systems. The first way is able to avoid the requirement of the upper bound of the first time derivation of control gain through introducing the modified integral-Lyapunov function. The second way defines the modulation function and quarentees fuzzy approach play a role only in the given closed region. Through using the adaptive compensation term of the optimal approximation error and the property of Nussbaum function, two ways avoid the requirement of a priori knowledge of the sign of the function control gain, the closed-loop control system is proved to be stable in the sense that all signals involved are bounded, with tracking error converging to zero.Secondly, based on the approximation capability of the second type of fuzzy logic system, variable structure adaptive fuzzy controller for uncertain nonlinear SISO /MIMO systems with unknown control gain sign and unknown dead-zone model is proposed, respectively. Based on the intuitive concept and piece-wise description of dead-zone model, the approach does not require the borders of dead-zone model parameters to be known through adaptive control term. In the process of design, we can avoid the requirement of the upper bound of the first time derivation of control gain and a priori knowledge of the sign of the function control gain through using the modified integral-Lyapunov function and Nussbaum function. In order to reduce the chatting in sliding model control, sign function is replaced by saturation function in control law. By theoretical analysis, the closed-loop control system is proved to be stable in the sense that all signals involved are bounded, with tracking error converging to zero.Finally, a design scheme of robust adaptive fuzzy controller for a class of perturbed strict-feedback nonlinear systems with unknown dead-zone model is proposed. The design is based on backstepping and the approximation capability of the first-type of fuzzy systems. By introducing characteristic function for the dead-zonemodel in the systems, a simplified dead-zone model is proposed. The approach removes the condition of the equal slope with defined region and does not require the borders of dead-zone model parameters to be known by adaptive control term. By the Lyapunov method, the closed-loop control system is proved to be semiglobally uniformly ultimately bounded, with tracking error converging to a neighborhood of zero.Through the research in this paper, the design and analysis problem for a class of uncertain nonlinear systems with unknown control gain sign has been properly solved .Numerical simulation experiments of these control schemes demonstrate their effectiveness.