This article deals with the design of an adaptive Controller for switched non-strict feedback nonlinear systems. In the studied system, the switching signal is arbitrary, the states are not measurable, and the signs of the Control gain functions that describe the Control directions are completely unknown. First, the unknown nonlinear functions in the switched system are approximated using the universal approximation theorem. Then, the unmeasured states are estimated using the linear state observer, and the Controller is designed through an adaptive back-stepping design procedure. Due to the appropriate change of coordinates, 1) neither fuzzy nor radial basis function is used in the design of the Controller, 2) only one adaptation law is designed to estimate the unknown parameters in the switched non-strict feedback nonlinear system, and 3) there is no Nussbaum function in the proposed adaptive Controller so, the large Control signal in the initial stages and the consequent damage to the actuators can be prevented. These features can lead to the simplicity of Controller design and the reduction of computational burden. Therefore, the proposed method can be used for practical systems. The stability of the closed-loop system is proved using Lyapunov stability theory. It is shown that, in addition to the semi-globally uniformly ultimately boundedness of all closed loop signals, the tracking error converges to a small neighborhood around zero. In the end, the efficiency of the proposed Control method is confirmed through the simulation results of an example.

In this paper, an adaptive fuzzy Control scheme is proposed for a class of perturbed strict-feedback nonlinear systems with unknown discrete and distributed time-varying delays, and the proposed design method does not require a priori knowledge of the signs of the Control gains. Based on the back-stepping technique, the adaptive fuzzy Controller is constructed. The main contributions of the paper are that (i) by constructing appropriate Lyapunov functionals and using the Nussbaum functions, the adaptive tracking Control problem is solved for the strict-feedback unknown nonlinear systems with the unknown discrete and distributed time-varying delays and the unknown Control directions (ii) the number of adaptive parameters is independent of the number of rules of fuzzy logic systems and system state variables, which reduces the computation burden greatly. It is proven that the proposed Controller guarantees that all the signals in the closed-loop system are bounded and the system output converges to a small neighborhood of the desired reference signal. Finally, an example is used to show the effectiveness of the proposed approach.