Abstract
In this paper, an adaptive neural control approach for a class of nonstrict-feedback nonlinear systems with unmodeled dynamic is presented. During the controller design process, the main difficulties arise from unknown functions and unmodeled dynamics, which are inevitable in practical applications. The unknown functions are approximated by utilizing the radial basis function neural networks' (RBF NNs) method, and for the problem of the unmodeled dynamics, a dynamic signal is introduced. The innovation of this paper is that we use the property of Gaussian functions to deal with the nonstrict-feedback form. Based on the above precondition, an adaptive NNs controller design scheme is developed by applying the backstepping recursive design. The proposed adaptive control approach guarantees that all the signals in closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighborhood around the origin by choosing appropriate parameters. In the end, a simulation example is provided to demonstrate the effectiveness of the proposed method.
Highlights
As is well known, nonlinear systems are ubiquitous in practical industrial process, such as chemical process, electrical power systems, metallurgical process, and so on
Among the proposed methods, backstepping technique plays an indispensable role in the design of adaptive control, because backstepping technique provides a systematic design methodology for nonlinear systems with strict feedback form, and many excellent results are reported in [1]–[12]
2) Compared with unknown nonlinear systems which are in strict-feedback form, an adaptive controller is constructed for a class of nonstrict-feedback nonlinear systems with unmodeled dynamic in this paper by using the nature of the Gaussian function
Summary
Nonlinear systems are ubiquitous in practical industrial process, such as chemical process, electrical power systems, metallurgical process, and so on. In [5], an adaptive NNs control scheme based on backstepping technique was proposed for a class pure-feedback nonlinear systems. The authors in [12], [22] proposed an adaptive fuzzy backstepping control approach for a class of uncertain nonlinear systems with strict-feedback form. Many researchers focus on the study of nonstrict-feedback systems Such as [24], an adaptive tracking controller was designed for a class of nonstrictfeedback nonlinear time-delay systems. 2) Compared with unknown nonlinear systems which are in strict-feedback form, an adaptive controller is constructed for a class of nonstrict-feedback nonlinear systems with unmodeled dynamic in this paper by using the nature of the Gaussian function. The main contributions of the proposed method are summarized as follows. 1) By using RBF NNs, the unknown functions are approximated properly, and this method does without the unknown functions linearized. 2) Compared with unknown nonlinear systems which are in strict-feedback form, an adaptive controller is constructed for a class of nonstrict-feedback nonlinear systems with unmodeled dynamic in this paper by using the nature of the Gaussian function. 3) This paper adopts a dynamic signal to handle the unmodeled dynamic and dynamic uncertainties to ensure the considered system can be controlled effectively
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