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AN oVERVIEW oF THE DEVELopMENT oF LoW GAIN FEEDBACK AND LoW-AND-HIGH GAIN FEEDBACK

Journal of Systems Science & Complexity 2009年第4期22卷 697-721页

作者： zongli lin department of electrical and computer engineering,university of virginia,p.o.box 400473,ch arlottesville,va 22904-4743,usa. department of electrical and computer engineering University of Virginia P.O. Box 400473 Charlottesville VA 22904-4743 USA

Low gain feedback refers to certain families of stabilizing state feedback gains that are pararaeterized in a scalar and go to zero as the scalar decreases to zero. Low gain feedback was initially proposed to achieve semi-global stabilization of linear systems subject to input saturation. It was then combined with high gain feedback in different ways for solving various control problems. The resulting feedback laws are referred to as low-and-high gain feedback. Since the introduction of low gain feedback in the context of semi-global stabilization of linear systems subject to input saturation, there has been effort to develop alternative methods for low gain design, to characterize key features of low gain feedback, and to explore new applications of the low gain and low-and-high gain feedback. This paper reviews the developments in low gain and low-and-high gain feedback designs.

关键词： Actuator saturation composite nonlinear feedback input saturation low-and-high gain feedback low gain feedback nonlinear control.

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Global practical stabilization of the double integrator system with an imperfect sensor and subject to a bounded disturbance

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Control Theory and Technology 2024年第3期22卷 468-478页

作者： Zhiyuan Zhu Yuanlong Li zongli lin department of Automation Shanghai Jiao Tong Universityand Key Laboratory of System Control and Information Processing of Ministry of EducationShanghai 200240China charles L.Brown department of electrical and computer engineering University of VirginiaP.0.Box 400743CharlottesvilleVA 22904-4743USA

This paper is concerned with global practical stabilization of the double integrator system with an imperfect sensor and subject to an additive bounded output *** imperfect sensor nonlinearity possesses the nonlinear characteristics of saturation and dead *** of the presence of output dead zone and the additive disturbance,the states cannot be expected to driven into an arbitrarily small neighborhood of the *** solve the global practical stabilization problem,we proposes a low gain-based linear dynamic output feedback law,under which the first state enters and remains in a bounded set whose size is depended on the bound of disturbance and the range of dead zone and the second state enters and remains in a pre-specified arbitrarily small set,both in finite *** results illustrate the effectiveness of our proposed control method.

关键词： output saturation Disturbance rejection output dead zone Low gain feedback-linear output feedback practical stabilization

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Low Gain and Low-and-High Gain Feedback:A Review and Some Recent Results

Low Gain and Low-and-High Gain Feedback:A Review and Some Re...

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2009中国控制与决策会议

作者： zongli lin charles L.Brown department of electrical and computer engineering,university of virginia,p.o.box 400473,charlottesville,va 22904-4743,usa.

＜正＞Low gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to *** gain feedback was initially proposed to achieve semi-global stabilization of linear systems subject to input *** was then combined with high gain feedback in different ways for solving various control *** resulting feedback laws are referred to as low-and-high gain *** the introduction of low gain feedback in the context of semi-global stabilization of linear systems subject to input saturation,there has been effort to develop alternative methods for low gain design, to characterize key features of low gain feedback,and to explore new applications of the low gain and low-and-high gain *** talk reviews the developments in low gain and low-and-high gain feedback *** of the results mentioned in the talk have appeared in the literature.A few recent results are still under review for publication.

关键词： Low gain feedback low-and-high gain feedback composite nonlinear feedback input saturation actuator saturation nonlinear control

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Design of multiple anti-windup loops for multiple activations

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Science china(Information Sciences) 2012年第9期55卷 1925-1934页

作者： WU XiongJun 1,2 & lin zongli 3,1 1 department of Automation,Shanghai Jiao Tong university,and Key Laboratory of System Control and Information processing,Ministry of Education of china,Shanghai 200240,china 2 No.802 Institute of Shanghai Academy of Space Flight Technology,the Eighth Academy of china Aerospace Science and Technology Corporation,Shanghai 200090,china 3 charles L.Brown department of electrical and computer engineering,university of virginia,p.o.box 400743,charlottesville,va 22904-4743,usa 1. department of Automation Shanghai Jiao Tong University and Key Laboratory of System Control and Information Processing Ministry of Education of China Shanghai 200240 China2. No. 802 Institute of Shanghai Academy of Space Flight Technology the Eighth Academy of China Aerospace Science and Technology Corporation Shanghai 200090 China3. Charles L. Brown Department of Electrical and Computer Engineering University of Virginia P.O. Box 400743 Charlottesville VA 22904-4743 USA

This paper considers anti-windup design for linear systems subject to actuator *** anti-windup gains are designed for activations immediately at the occurrence actuator saturation,after the saturation has reached a certain level and in anticipation of the occurrence of saturation,*** design is based on the minimization of L 2 gain from the disturbance to the controlled output of the resulting closed-loop *** anti-windup scheme involves a single anti-windup loop for immediate activation.A recent innovation is to design a single anti-windup loop for delayed or anticipatory activation,as well as to design two anti-windup gains,one for immediate activation and one for delayed *** design of three anti-windup gains for three different activations is shown through simulation to lead to significant further performance improvement over the previous activation schemes.

关键词： actuator saturation anti-windup anticipatory activation delayed activation L 2 gain nonlinear control

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linear Systems Toolkit in Matlab: Structural Decompositions and Their Applications

Linear Systems Toolkit in Matlab: Structural Decompositions ...

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第二十四届中国控制会议

作者： Xinmin Liu~1 Ben M. chen~2 zongli lin~1 ~1charles L. Brown department of electrical and computer engineering, university of virginia, p. o. box 400473, charlottesville, va 22904-4743, usa.~2department of electrical and computer engineering, National university of Singapore, Singapore 117576, Republic of Singapore

This paper presents a brief description of the software toolbox, linear Systems Toolkit, developed in the MATLAB environment. The toolkit contains 66 m-functions, including structural decompositions of linear autonomous systems,unforced/unsensed systems, proper systems, and singular systems, along with their applications to system factorizations, sensor/actuator selection, H and Hcontrol, and disturbance deeoupling problems. The toolkit is available for free at websites: http://*** and http://***/mchen.

关键词： linear systems structural decompositions linear control software development.

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Set Invariance Conditions for Singular linear Systems Subject to Actuator Saturation

Set Invariance Conditions for Singular Linear Systems Subjec...

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第25届中国控制会议

作者： lin zongli,Lv Liang charles L. Brown department of electrical and computer engineering, university of virginia,p.o.box 400743, charlottesville,va 22904-4743,U. S. A. department of Automation,Shanghai Jiao Tong university,Shanghai,china

＜正＞In this paper,we establish a set of conditions under which an ellipsoid is contractively invariant with respect to a singular linear system under a saturated linear feedback. These conditions can be expressed in terms of linear matrix inequalities,and the largest constrictively invariant ellipsoid can be determined by solving an optimization problem with LMI constraints. By viewing the feedback gain as an additional variable,this optimization problem can be readily adapted for the design of feedback gain that results in the largest contractively invariant ellipsoid. Moreover,in the degenerate case where the singular linear system reduces to a regular system,our set invariance conditions reduce to the existing set invariance conditions for normal linear systems.

关键词： singular systems set invariance actuator saturation

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Design of Multiple Anti-windup Loops for Multiple Activations

Design of Multiple Anti-windup Loops for Multiple Activation...

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第三十届中国控制会议

作者： WU Xiongjun~1,lin zongli~2 1.department of Automation,Shanghai Jiao Tong university,and Key Laboratory of System Control and Information processing, Ministry of Education of china,Shanghai 200240,p.R.china 2.charles L.Brown department of electrical and computer engineering,university of virginia, p.o.box 400743,charlottesville,va 22904-4743,usa

关键词： Actuator saturation Anti-windup Anticipatory activation Delayed activation L2 gain

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Analysis and Design of Singular linear Systems under Actuator Saturation and L2/L∞ Disturbances

Analysis and Design of Singular Linear Systems under Actuato...

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第二十七届中国控制会议

作者： Lv Liang1,lin zongli2 1.department of Automation,Shanghai Jiao Tong university,800 Dongchuan Rd,Shanghai 200240,p.R.china. 2.charles L.Brown department of electrical and computer engineering,university of virginia,p.o.box 400743,charlottesville,va 22904-4743,U.S.A.

This paper carries out an analysis of the L2 gain and L∞performance for singular linear systems under actuator *** notion of bounded state stability（BSS） with respect to the influence of L2 or L∞disturbances is introduced and conditions under which a system is bounded state stable are established in terms of linear matrix inequalities（LMIs） .The disturbance tolerance capability of the system is then measured as the bound on the L2 or L∞norm of the disturbances under which the system remains bounded state stable and the disturbance rejection capability is measured by the restricted L2 gain from the disturbance to the system output or L∞norm of the system *** on the BSS conditions,the assessment of the disturbance tolerance and rejection capabilities of the system under a given state feedback law is formulated and solved as LMI constrained optimization *** viewing the feedback gain as an additional variable,these optimization problems can be readily adapted for control *** analysis and design reduce to the existing results for regular linear systems in the degenerate case where the singular linear system reduces to a regular system,and to the existing results for singular systems in the absence of actuator saturation or when the disturbance is weak enough to not cause saturation.

关键词： Singular systems L2 gain L∞ performance Disturbance tolerance Disturbance rejection Actuator saturation

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An H∞ Control Based Receding Horizon Control Scheme for linear Systems Subject to Input Saturation

An H∞ Control Based Receding Horizon Control Scheme for Lin...

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第二十九届中国控制会议

作者： WU Xiongjun1,lin zongli2,XI Yugeng1,LI Dewei1 1.department of Automation,Shanghai Jiao Tong university,Shanghai 200240,p.R.china 2.charles L.Brown department of electrical and computer engineering,university of virginia,p.o.box 400743,charlottesville,va 22904-4743,usa

This paper proposes an H∞control based receding horizon control design scheme for discrete-time linear systems subject input saturation and external L2 *** are established under which the state trajectories of the closed-loop starting from an ellipsoid remain within another larger ellipsoid and the restricted L2 gain from the disturbance to the controlled output over a class of L2 disturbances with a given bound on their energies is no greater than a given *** conditions allow the saturation to occur and reveal a clear trade-off between the sizes of the ellipsoids and the level of the restricted L2 gain,which motivates the adoption of the receding horizon control design *** each time instant,the control design is formulated as an LMI optimization *** state feedback and output feedback are considered.

关键词： Constrained Control Input Saturation L2 Gain Receding Horizon Control

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A parametric Lyapunov Equation Approach to the Design of Low Gain Feedback

A Parametric Lyapunov Equation Approach to the Design of Low...

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第二十六届中国控制会议

作者： Zhou Bin1,Duan Guangren1,lin zongli2 1.Center for Control Theory and Guidance Technology,Harbin Institute of Technology,p.o.box 416,Harbin,Heilongjiang 150001,p.R.china2.charles L.Brown department of electrical and computer engineering,university of virginia,p.o.box 400743,charlottesville,va22904-4743,U.S.A.

Low gain feedback has found several applications in constrained control systems,robust control and nonlinear *** gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to *** feedback gains can be constructed either by an eigenstructure assignment algorithm or through the solution of a parametric algebraic Riccati equation （ARE）.The eigenstructure assignment approach leads to feedback gains in the form of a matrix polynomial in the parameter,while the ARE approach requires the solution of an ARE for each value of the *** paper proposes an alternative approach to low gain feedback design based on the solution of a parametric Lyapunov *** an approach possesses the advantages of both the eigenstructure assignment approach and the ARE based *** also avoids the possible numerical stiffness in solving a parametric ARE and the structural decomposition of the open loop system that is required by the eigenstructure assignment approach.

关键词： low gain feedback actuator saturation semi-global stabilization global stabilization set invariance parametric Lyapunov equation

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