Adaptive Fuzzy Prescribed Performance Control of Nontriangular Structure Nonlinear Systems

In this article, a new n-step fuzzy adaptive output tracking prescribed performance control problem is investigated for a class of nontriangular structure nonlinear systems. In the control design process, the mean value theorem is used to separate the virtual state variables needed for the control design, and the implicit function theorem is exploited to assert the existence of the desired continuous control. The fuzzy logic systems are used to identify the unknown nonlinear functions and ideal controller, respectively. By constructing a novel iterative Lyapunov function, a new n-step adaptive backstepping control design algorithm is established. The prominent characteristics of the proposed adaptive fuzzy backstepping control design algorithm are as follows: one is that it can ensure the closed-loop control system is the semiglobally uniformly ultimately bounded and the tracking error can converge within the prescribed performance bounds. The other is that it solves the controller design problem for the nontriangular nonlinear systems that the previous adaptive backstepping design techniques cannot deal with. Two examples are provided to show the effectiveness of the presented control method.