A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

Abstract

Summary This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.

Adaptive finite‐time tracking control for output‐constrained nonlinear systems with non‐strict‐feedback structure

“…Therefore, the system structure is more general than the previous results. In addition, different from these works [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][35][36][37][38][39][40][41][42][43][44][45][46][47][48] this article presents another challenge: how to handle the phenomenon of output constraints.…”

“…Theorem 1. Based on Assumption 1, think about the system (4), under the action of the virtual control signals (7) and (8), the controller (9), and the parameter adaptive law (10), it has the following properties:…”

“…Therefore, the system structure is more general than the previous results. In addition, different from these works , this article presents another challenge: how to handle the phenomenon of output constraints.…”

“…Over the past few decades, the design of backstepping control has become the basic method of nonlinear cascade system control, and remarkable achievements have been made . In addition, neural networks and fuzzy logic systems, as two universal approximators, have been widely used for the modeling of unknown nonlinear functions, and adaptive controllers were designed in References by combining adaptive technique with backstepping. Although some great developments have been made in References , the problem of output constraints is not considered.…”

“…The existing results in References cannot be directly applied to our article, since these works do not consider the output constraint effects. In addition, in comparison with the current literatures on constrained systems, a series of finite‐time control schemes were constructed in References .…”