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.

This paper addresses the problem of adaptive fuzzy tracking Control for a class of nonlinearly parameterized systems with unknown Control directions. In this paper, the nonlinearly parameterized functions are lumped into the unknown continuous functions which can be approximated by using the fuzzy logic systems (FLS) in Mamdani type. Then, the Nussbaum-type function is used to detect the unknown Control direction and based on the backstepping technique, the adaptive fuzzy Controller is designed. The main advantages of this paper are that (1) in the existing results the separation principle is used to deal with the nonlinearly parameterized functions, unlike them in this paper, the FLS are applied to approximate the nonlinearly parameterized functions, (2) by using the minimal learning parameters (MLP) algorithm, only one parameter needs to be adjusted online in the Controller design procedure, which reduces the online computation burden greatly, (3) the Nussbaum-gain technique is introduced to resolve the unknown Control direction problems. It is proven that the proposed Control scheme renders the closed-loop system stable in the sense of semiglobal uniformly ultimately bounded (UUB). Finally, simulation results are provided to show the effectiveness of the proposed approach.

A common method for Controlling a group of parallel converters in decentralized Control strategy structure in an island microgrid, the use is the droop-down characteristics of frequency ω-P and voltage E-Q. However, the problem with using this method is that the reactive power is not properly distributed (in proportion to the capacity of the micronutrients) between the micronutrients, which may lead to overload in the converters. Microgrids may also suffer from dynamic stability problems such as power fluctuations, which can be increased by switching between active and reactive power Control. To avoid this problem, the X / R ratio of transmission lines is an important parameter that should be carefully considered in the design of micronutrient Controllers. By linearizing and simplifying conditions, the Control system conversion function model becomes a single input-single output system, which is efficient enough to show the relationship between Control parameters such as slope of droop characteristics and derivative sentences, virtual impedance, and voltage Controllers. Using this model, stability conditions for different parameters are analyzed. Also, to improve power distribution stability, common droop strategies are modified by adjusting the slope as well as adding nonlinear sentence sections. This approach reduces the coupling between active and reactive power Control and reduces the dependence of power distribution on grid parameters such as the X / R ratio. To evaluate the reliability of the proposed model, the simulation results in a sample island microgrid in MATLAB software are presented.

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.