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An Overview of Finite/Fixed-Time Control and Its Application in Engineering Systems

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IEEE/CAA Journal of Automatica Sinica 2022年第12期9卷 2106-2120页

作者： Yang Liu Hongyi Li Zongyu Zuo Xiaodi Li Renquan Lu IEEE College of Automation and Electronics Engineering Qingdao University of Science and TechnologyQingdao 266061 School of Automation Guangdong University of TechnologyGuangzhou 510006China School of Automation Guangdong University of Technologyand also with the Guangdong Province Key Laboratory of Intelligent Decision and Cooperative ControlGuangzhou 510006China School of Automation Science and Electrical Engineering Beihang UniversityBeijing 100083China School of Mathematics and Statistics Shandong Normal UniversityBeijing 100083China Center for Control and Engineering Computation Shandong Normal UniversityJinan 250014China

The finite/fixed-time stabilization and tracking control is currently a hot field in various systems since the faster convergence can be obtained. By contrast to the asymptotic stability,the finite-time stability possesses the better control performance and disturbance rejection property. Different from the finite-time stability, the fixed-time stability has a faster convergence speed and the upper bound of the settling time can be estimated. Moreover, the convergent time does not rely on the initial *** work aims at presenting an overview of the finite/fixed-time stabilization and tracking control and its applications in engineering systems. Firstly, several fundamental definitions on the finite/fixed-time stability are recalled. Then, the research results on the finite/fixed-time stabilization and tracking control are reviewed in detail and categorized via diverse input signal structures and engineering applications. Finally, some challenging problems needed to be solved are presented.

关键词： adding a power integrator finite/fixed-time control and application homogeneous theory sliding mode control

维普期刊数据库

Continuous output-feedback stabilization for a class of stochastic high-order nonlinear systems

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控制理论与应用（英文版） 2013年第3期11卷 343-350页

作者： Jian ZHANG Yungang LIU School of Control Science and Engineering Shandong University Department of Mathematics Zhengzhou University

This paper is concerned with the global stabilization via output-feedback for a class of high-order stochastic nonlinear systems with unmeasurable states dependent growth and uncertain control coefficients. Indeed, there have been abundant deterministic results which recently inspired the intense investigation for their stochastic analogous. However, because of the possibility of non-unique solutions to the systems, there lack basic concepts and theorems for the problem under investigation. First of all, two stochastic stability concepts are generalized to allow the stochastic systems with more than one solution, and a key theorem is given to provide the sufficient conditions for the stochastic stabilities in a weaker sense. Then, by introducing the suitable reduced order observer and appropriate control Lyapunov functions, and by using the method of adding a power integrator, a continuous （nonsmooth） output-feedback controller is successfully designed, which guarantees that the closed-loop system is globally asymptotically stable in probability.

关键词： Stochastic nonlinear systems Uncertain control coefficients Nonsmooth stabilization Output-feedback control adding a power integrator

维普期刊数据库

Output feedback stabilization for power-integrator systems with unknown measurement sensitivity

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Science China(Information Sciences) 2021年第9期64卷 252-254页

作者： Yu SHAO Zong-Yao SUN Xue-Jun XIE Zhen-Guo LIU Institute of Automation Qufu Normal University Department of Automation Shanxi University

Dear editor,The technical limitations on sensors mean that some state variables will not be detected in any controlled system, so the actual values of an output function will always deviate somewhat from the nominal values. A practical example was given in [1], where the output of an infrared sensor that measures the distance between parts in a magnetic bearing suspension system suffers from measurement error [1].

关键词： Output feedback homogeneous observer unknown measurement sensitivity adding a power integrator reduced-order observer

A Continuous State Feedback Controller Design for High-order Nonlinear Systems with Polynomial Growth Nonlinearities

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International Journal of Automation and computing 2013年第4期10卷 267-274页

作者： Guo-Dong Zhao Na Duan School of Control Science and Engineering Shandong University School of Electrical Engineering and Automation Jiangsu Normal University

In this paper, we investigate the problem of global stabilization for a general class of high-order and non-smoothly stabilizable nonlinear systems with both lower-order and higher-order growth conditions. The designed continuous state feedback controller is recursively constructed to guarantee the global strong stabilization of the closed-loop system.

关键词： Nonlinear systems lower-order and high-order nonlinearities state feedback adding a power integrator global strong stabilization.

维普期刊数据库

A new approach to adaptive control design without overparametrization for a class of uncertain nonlinear systems

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Science China(Information Sciences) 2011年第7期54卷 1419-1429页

作者： ZHANG Jian & LIU YunGang School of Control Science and Engineering,Shandong University,Jinan 250061,China School of Control Science and Engineering Shandong University

This paper considers the globally stabilizing adaptive controller design for a class of more general uncertain high-order nonlinear systems with unknown control *** the existing literature has solved the problem,for n-dimensional systems,the existing methods need at least n + 1 dynamic updating laws for the unknown parameters to construct the stabilizing adaptive controller;that is,the dimension of the dynamic compensator is not less than n + 1,and therefore,there exists serious *** this paper,by defining some new unknown parameters which need dynamic updating,also by using adding a power integrator and related adaptive technique,the overparametrization is successfully solved and a new approach is given to design stabilizing adaptive controller based on only one parameter updating law.A simulation example is finally provided to demonstrate the validness of the proposed approach.

关键词： high-order nonlinear systems unknown control coefficients overparametrization stabilizing con- trol design adding a power integrator adaptive technique

Global control for a class of uncertain upper-triangular nonlinear systems with uncontrollable linearization

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Global control for a class of uncertain upper-triangular non...

第36届中国控制会议

作者： Zha Wenting Qian Chunjiang Zhai Junyong Fei Shumin School of Mechanical Electronic & Information Engineering China University of Mining & Technology (Beijing) Key Laboratory of Measurement and Control of CSE Ministry of EducationSchool of AutomationSoutheast University Department of Electrical and Computer Engineering The University of Texas at San Antonio

ISBN: (纸本)9781538629185

This paper fucuses on the global control problem for a class of upper-triangular nonlinear systems whose linearization around the origin is not guaranteed to be controllable. Assuming that the nonlinearities satisfy the homogeneous growth conditions, a nonsmooth state-feedback controller is elaborately constructed based on the adding a power integrator technique and the homogeneous domination approach. By introducing the dynamic gain to deal with the input dependent growth rate, it can be proved that all the signals of the closed-loop system are bounded and the system states converge to the origin asymptotically.

关键词： upper-triangular nonlinear systems input dependent growth rate adding a power integrator homogeneous domination approach

Adaptive stabilization of High-order Nonholonomic Systems with Unknown Control Coefficients

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Adaptive stabilization of High-order Nonholonomic Systems wi...

第三十届中国控制会议

作者： ZHANG Jian,LIU Yungang School of Control Science and Engineering,Shandong University,Jinan 250061,P.R.China

＜正＞This paper solves the problem of globally stabilizing adaptive control design for a class of high-order nonholonomic systems,by skillfully using the discontinuous transformation of coordinates and the method of adding a power *** with the existing literature,the control coefficients of the systems are unknown and no known constants can（lower and upper） bound them,and in the designed adaptive controller,only one updating law is needed to dynamically compensate the unknowns in the system control coefficients.A numerical simulation is provided to demonstrate the validness of the proposed method.

关键词： High-order nonholonomic system Stabilizing adaptive control design Switching control strategy adding a power integrator

State-Feedback Adaptive Stabilizing Control Design for a Class of High-Order Nonlinear Systems with Unknown Control Coefficients

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State-Feedback Adaptive Stabilizing Control Design for a Cla...

第25届中国控制会议

作者： Sun Zongyao,Liu Yungang School of Control Science and Engineering,Shandong University,Jinan 250061

＜正＞In this paper,a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients , whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper, without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin,but also guarantees the globally asymptotic stability of the closed-loop states and the uniform boundedness of all the other closedloop signals.

关键词： High-order nonlinear systems Unknown control coefficients State-feedback adaptive stabilizing control adding a power integrator Tuning functions

An Adaptive Controller for a Class of High-Order Nonlinear Systems with Unknown Control Coefficients

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An Adaptive Controller for a Class of High-Order Nonlinear S...

第三十届中国控制会议

作者： SUN Zongyao~1,LIU Yungang~2,LIU Zhenguo~1 1.Institute of Automation,Qufu Normal University,Qufu,273165,P.R.China 2.School of Control Science and Engineering,Shandong University,Jinan,250061,P.R.China

＜正＞In this paper,a valid approach is successfully addressed to design the adaptive stabilizing control law for a class of high-order nonlinear systems with unknown control coefficients and in triangular *** such control systems,the state- feedback stabilizing control has been investigated recently under the assumption that the lower bounds of the control coefficients are precisely *** paper removes such assumption,and gives the recursive design procedure of stabilizing control law by employing the approach of adding a power integrator together with adaptive technique to the appropriately defined unknown system *** designed state-feedback adaptive control law,which vanishes at the origin,guarantees that the states of the closed-loop system are globally asymptotically stable,while all the other signals are uniformly bounded.

关键词： High-Order nonlinear systems Adaptive stabilizing control adding a power integrator Tuning functions