• Title/Summary/Keyword: Lyapunov-based control

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Nonlinear Adaptive Control based on Lyapunov Analysis: Overview and Survey (리아프노브 분석법 기반 비선형 적응제어 개요 및 연구동향 조사)

  • Park, Jin Bae;Lee, Jae Young
    • Journal of Institute of Control, Robotics and Systems
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    • v.20 no.3
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    • pp.261-269
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    • 2014
  • This paper provides an overview of the basics and recent studies of Lyapunov-based nonlinear adaptive control, the aim of which is to improve or maintain the performance and stability of the closed-loop system by cancelling out the presumable uncertainties in the nonlinear system dynamics. The design principles are essentially based on Lyapunov's direct method. In this survey, we provide a comprehensive overview of Lyapunov-based nonlinear adaptive control techniques with simplified effective design examples, which are to be elaborated as related recent results are gradually shown. The scope of the survey contains research on singularity problems in adaptive control, the techniques to deal with linearly and nonlinearly parameterized uncertainties, robust neuro-adaptive control, and adaptive control methodologies combined with various nonlinear control techniques such as sliding-mode control, back-stepping, dynamic surface control, and optimal/$H_{\infty}$ control.

Performance Improvement of Model Predictive Control Using Control Error Compensation for Power Electronic Converters Based on the Lyapunov Function

  • Du, Guiping;Liu, Zhifei;Du, Fada;Li, Jiajian
    • Journal of Power Electronics
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    • v.17 no.4
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    • pp.983-990
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    • 2017
  • This paper proposes a model predictive control based on the discrete Lyapunov function to improve the performance of power electronic converters. The proposed control technique, based on the finite control set model predictive control (FCS-MPC), defines a cost function for the control law which is determined under the Lyapunov stability theorem with a control error compensation. The steady state and dynamic performance of the proposed control strategy has been tested under a single phase AC/DC voltage source rectifier (S-VSR). Experimental results demonstrate that the proposed control strategy not only offers global stability and good robustness but also leads to a high quality sinusoidal current with a reasonably low total harmonic distortion (THD) and a fast dynamic response under linear loads.

A V-Shaped Lyapunov Function Approach to Model-Based Control of Flexible-Joint Robots

  • Lee, Ho-Hoon;Park, Seung-Gap
    • Journal of Mechanical Science and Technology
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    • v.14 no.11
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    • pp.1225-1231
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    • 2000
  • This paper proposes a V-shaped Lyapunov function approach for the model-based control of flexible-joint robots, in which a new model-based nonlinear control scheme is designed based on a V-shaped Lyapunov function. The proposed control guarantees global asymptotic stability for link trajectory control while keeping all internal signals bounded. Since joint flexibility is used as a control parameter, the proposed control is not restricted by the degree of joint flexibility and be applied to flexibility-joint, partly-flexibility, or rigid-joint robots without modification. the effectiveness of the proposed control has been by computer simulation.

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Design of Lyapunov Theory based State Feedback Controller for Time-Delay Systems (시간지연 시스템을 위한 리아푸노브 이론 기반 상태 피드백 제어기 설계)

  • Cho, Hyun Cheol;Shin, Chan Bai
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.62 no.1
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    • pp.95-100
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    • 2013
  • This paper presents a new state feedback control approach for communication networks based control systems in which control input and output observation time-delay natures are generally occurred in practice. We first establish a generic state feedback control framework based on well-known linear system theory. A maximum time-delay value which allows critical stability of whole control system are defined to make a positive definite Lyapunov function which is mathematically composed of controlled system states. We analytically derive its control parameters by using a steepest descent optimization method in order to guarantee a stability condition through Lyapunov theory. Computer simulation is numerically carried out for demonstrating reliability of the proposed NCS algorithm and a comparative study is accomplished to prove its superiority for which the traditional control approach for NCS is made use of under same simulation scenarios.

Robust Stable Conditions Based on the Quadratic Form Lyapunov Function (2차 형식 Lyapunov 함수에 기초한 강인한 안정조건)

  • Lee, Dong-Cheol;Bae, Jong-Il;Jo, Bong-Kwan;Bae, Chul-Min
    • Proceedings of the KIEE Conference
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    • 2004.07d
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    • pp.2212-2214
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    • 2004
  • Robust stable analysis with the system bounded parameteric variation is very important among the various control theory. This study is to investigate the robust stable conditions using the quadratic form Lyapunov function in which the coefficient matrix is affined linear system. The quadratic stability using the quadratic form Lyapunov function is not investigated yet. The Lyapunov unction is robust stable not to be dependent by the variable parameters, which means that the Lyapunov function is conservative. We suggest the robust stable conditions in the Lyapunov function in which the variable parameters are dependent in order to reduce the conservativeness of quadratic stability.

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Robust Optimal Bang-Bang Controller Using Lyapunov Robust Stability Condition (Lyapunov 강인 안정성 조건을 이용한 강인 최적 뱅뱅 제어기)

  • Park Young-Jin;Moon Seok-Jun;Park Youn-Sik;Lim Chae-Wook
    • Journal of Institute of Control, Robotics and Systems
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    • v.12 no.5
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    • pp.411-418
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    • 2006
  • There are mainly two types of bang-bang controllers for nominal linear time-invariant (LTI) system. Optimal bang-bang controller is designed based on optimal control theory and suboptimal bang-bang controller is obtained by using Lyapunov stability condition. In this paper, the suboptimal bang-bang control method is extended to LTI system involving both control input saturation and structured real parameter uncertainties by using Lyapunov robust stability condition. Two robust optimal bang-bang controllers are derived by minimizing the time derivative of Lyapunov function subjected to the limit of control input. The one is developed based on the classical quadratic stability(QS), and the other is developed based on the affine quadratic stability(AQS). And characteristics of the two controllers are compared. Especially, bounds of parameter uncertainties which theoretically guarantee robust stability of the two controllers are compared quantitatively for 1DOF vibrating system. Moreover, the validity of robust optimal bang-bang controller based on the AQS is shown through numerical simulations for this system.

Control of Variable Reluctance Motors: A Comparison between Classical and Lyapunov-Based Fuzzy Schemes

  • Filizadeh, S.;Safavian, L.S.;Emadi, A.
    • Journal of Power Electronics
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    • v.2 no.4
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    • pp.305-311
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    • 2002
  • In this paper, two approaches for designing tracking controllers for a variable reluctance motor (VRM), namely the Lyapunov-based fuzzy approach and the classical approach, are compared. The nonlinear model of a VRM is first addressed. The two control schemes are introduced afterwards, and then applied to obtain tracking controllers. Simulation results of a sample case, to which the methods are applied, are also presented. Comparison of the methods based on the results obtained concludes the paper.

A LYAPUNOV CHARACTERIZATION OF ASYMPTOTIC CONTROLLABILITY FOR NONLINEAR SWITCHED SYSTEMS

  • Wang, Yanling;Qi, Ailing
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.1-11
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    • 2014
  • In this paper, we show that general nonlinear switched systems are asymptotically controllable if and only if there exist control-Lyapunov functions for their relaxation systems. If the switching signal is dependent on the time, then the control-Lyapunov functions are continuous. And if the switching signal is dependent on the state, then the control-Lyapunov functions are $C^1$-smooth. We obtain the results from the viewpoint of control system theory. Our approach is based on the relaxation theorems of differential inclusions and the classic Lyapunov characterization.

A Nonlinear Model-Based Anti-Swing Control for Overhead Cranes with High Hoisting Speeds (권상/권하 속도가 큰 경우 크레인의 비선형 무진동 제어)

  • Lee, Ho-Hun;Jeon, Jong-Hak;Choe, Seung-Gap
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.25 no.9
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    • pp.1461-1467
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    • 2001
  • This paper proposes a new approach for the ant-swing control of overhead cranes. The proposed control consists of a model-based anti-swing control scheme and a practical path planning scheme. The anti-swing control scheme is designed based on the Lyapunov stability theorem; the proposed control does not require the usual constraints of small load mass, small load swing, slow hoisting speed, and small hoisting distance, but guarantees asymptotic stability while keeping all internal signals bounded. The path planning scheme is designed based on the concepts of minimum-time control and anti-swing control; the proposed path planning generates near-minimum-time trajectories independently of hoisting speed and distance. The effectiveness of the proposed control is shown by computer simulation.

Three-axis Attitude Control for Flexible Spacecraft by Lyapunov Approach under Gravity Potential

  • Bang, Hyo-Choong;Lee, Kwang-Hyun;Lim, Hyung-Chul
    • International Journal of Aeronautical and Space Sciences
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    • v.4 no.1
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    • pp.99-109
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    • 2003
  • Attitude control law synthesis for the three-axis attitude maneuver of a flexible spacecraft model is presented in this study. The basic idea is motivated by previous works for the extension into a more general case. The new case includes gravitational gradient torque which has significant effect on a wide range of low earth orbit missions. As the first step, the fully nonlinear dynamic equations of motion are derived including gravitational gradient. The control law design based upon the Lyapunov approach is attempted. The Lyapunov function consists of a weighted combination of system kinetic and potential energy. Then, a set of stabilizing control law is derived from the basic Lyapunov stability theory. The new control law is therefore in a general form partially validating the previous work in some sense.