Adaptive Fuzzy Controller for a Class of Uncertain Nonlinear Systems

In general, the state feedback control gain can be obtained by solving certain linear matrix inequalities (LMIs) when using the Takagi-Sugeno (T-S) fuzzy model to develop a control system. In this paper, the reconstruction error between the real system to be controlled and its T-S fuzzy model, which consists of parameter uncertainties and external disturbance, is considered. As a result, we arrive at an adaptive controller that has two parts: one is obtained by solving certain LMIs (fixed part) and another one is acquired by an adaptive law (variable part). The proposed controller can guarantee the control state to converge and uniformly bounded while maintaining all the signals involved stable. Also, the convergence and boundedness in terms of relaxing the LMIs conservatism are discussed. An inverted pendulum is provided to demonstrate the effectiveness of the proposed adaptive fuzzy controller.