Adaptive Control And Application For High-Order Nonlinear Systems With Unknown Input Powers

How to control the various non-linear systems in the world has always been relevant to people’s lives and to the advancement of technology.Among them,scholars have gradually gained a deeper understanding of the more specific strict feedback systems.In the course of the ongoing in-depth study of non-linear systems with strict feedback properties,higher order non-linear systems,as a development of strict feedback systems,have become noteworthy objects of study.For the purposes of this paper,non-linear systems with values of the input powers of the individual state equations larger than ’1’ are classified as higher order non-linear systems.It is because the input powers of higher order non-linear systems are greater than ’1’that additional terms arise in the stability analysis compared to common systems,and these additional terms cause additional difficulties in the design of the system controller.It is worth noting that the control problems associated with such systems will be even more difficult and challenging when there is uncertainty in the system,for example,when the input power is unknown.In recent years,many experts and scholars have studied and obtained fruitful results on various types of higher order non-linear systems.However,for higher order non-linear systems with uncertainty,especially when the input power of the system is unknown,the relevant research is not sufficient and needs to be further explored.In this paper,the control problem of uncertain nonlinear systems with unknown system input powers is investigated and a corresponding control scheme is proposed.The details are as follows:Firstly,a class of second-order nonlinear systems with unknown input powers is studied,its tracking control problem is considered,and an adaptive robust control method is proposed to ensure that the output of this system asymptotically tracks the reference signal provided.Based on Lyapunov stability theory,it is shown that the tracking error converges to a small adjustable neighborhood of the origin.Finally,the feasibility and effectiveness of the control scheme proposed in this paper are verified by numerical simulations.Secondly,the tracking control problem of a class of high-order nonlinear systems with unknown input powers is discussed.In order to ensure that the output of this system can asymptotically track the reference signal,a back-propagation adaptive control method is proposed.Based on Lyapunov stability theory,it is shown that the tracking error converges asymptotically to an adjustable neighborhood of the origin.The method improves some of the shortcomings of existing results and relaxes some of the assumptions imposed on the system,while extending the system to the higher order case.Finally,the feasibility and effectiveness of the control method proposed in this paper is verified by numerical simulations.Thirdly,the adaptive tracking control problem for a class of highly uncertain nonlinear systems with unknown input powers and higher order forms is investigated.Based on the classical sliding mode control method,a neural network is used to approximate the smooth unknown function,which effectively compensates for the uncertainty of the system.In this paper,a neural network-based adaptive sliding mode control scheme is successfully designed to ensure that all signals of the resulting closed-loop system are globally bounded and that the tracking error eventually converges to a very small neighborhood of the origin.Simulation examples verify the effectiveness of the proposed sliding mode adaptive controller.