• 제목/요약/키워드: Theorem Lyapunov

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Observer-based Distributed Consensus Algorithm for Multi-agent Systems with Output Saturations

  • Lim, Young-Hun;Lee, Gwang-Seok
    • Journal of information and communication convergence engineering
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    • 제17권3호
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    • pp.167-173
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    • 2019
  • This study investigates the problem of leader-following consensus for multi-agent systems with output saturations. This study assumes that the agents are described as a neutrally stable system, and the leader agent generates the bounded trajectory within the saturation level. Then, the objective of the leader-following consensus is to track the trajectory of the leader by exchanging information with neighbors. To solve this problem, we propose an observer-based distributed consensus algorithm. Then, we provide a consensus analysis by applying the Lyapunov stability theorem and LaSalle's invariance principle. The result shows that the agents achieve the leader-following consensus in a global sense. Moreover, we can achieve the consensus by choosing any positive control gain. Finally, we perform a numerical simulation to demonstrate the validity of the proposed algorithm.

STABILITYANALYSIS OF LINGUISTIC FUZZY MODEL SYSTEMS IN STATESPACE

  • Kim, Won C.;Woo
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 1993년도 Fifth International Fuzzy Systems Association World Congress 93
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    • pp.953-955
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    • 1993
  • In this paper we propose a new stability theorem and a robust stability condition for linguistic fuzzy model systems in state space. First we define a stability in linear sense. After representing the fuzzy model by a system with disturbances, A necessary and sufficient condition for the stability is derived. This condition is proved to be a sufficient condition of the fuzzy model. The Q in the Lyapunov equation is iteratively adjusted by an gradient-based algorithm to improve its stability test. Finally, stability robustness bounds of a system having modeling error is derived. An example is also included to show that the stability test is powerful.

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퍼지 슬라이딩 모드의 속도 향상을 위한 제어기 설계 (Fuzzy sliding mode controller design for improving the learning rate)

  • 황은주;조영완;김은태;박민용
    • 한국지능시스템학회논문지
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    • 제16권6호
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    • pp.747-752
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    • 2006
  • 본 논문에서는 두 개의 시스템으로 구성된 적응 퍼지 슬라이딩 모드 제어기의 설계를 제안한다. 제안한 슬라이딩 모드 제어기는 두 개의 시스템입력으로 구성된다. 기존의 슬라이딩 모드 제어기는 $approximation{\^{u}}(t)$에 불연속항 sgn함수나 sat함수를 추가하여 상태궤적을 sliding surface로 보내는 제어 기법을 사용하고 있다. 본 논문에서는 이러한 기존의 제어기에 또 하나의 불연속항 제어기를 추가하여 불확실한 제어 이득에 의한 disturbance를 줄여주고, 불확실한 외란에 강인한 제어기설계와 알지 못하는 실제 비선형 시스템과 퍼지 시스템 간의 오차에 의한 불안정성도 해결할 수 있는 제어기를 제안하였다. 또한 본 논문에서는 Fuzzy tuning을 통해 슬라이딩 조건을 가변화함으로써 기존의 슬라이딩 모드 제어기에 비해 빠르고 정확하게 추종 가능하도록 제어기의 성능을 향상시킨다. 기존의 슬라이딩 모드 제어방식에서는 ${\eta}$값을 임의의 양의 상수로 두고 설계를 하였다. 하지만 이러한 방식은 높은 overshoot를 발생하게 하거나 늦은 정정시간을 갖게 하였다. 이를 해결하기 위하여 본 논문에서는 state의 각 상황에 맞는 ${\eta}$값을 fuzzy tuning을 통하여 유도해 내어 overshoot를 줄이며 동시에 정정시간도 줄여 제어성능을 높이는 방법을 제안한다.

Formation Flight and Collision Avoidance for Multiple UAVs using Concept of Elastic Weighting Factor

  • Kang, Seunghoon;Choi, Hyunjin;Kim, Youdan
    • International Journal of Aeronautical and Space Sciences
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    • 제14권1호
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    • pp.75-84
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    • 2013
  • In this paper, the guidance law for formation flight and collision avoidance of multiple Unmanned Aerial Vehicle (UAV)s is proposed. To construct the physically comprehensible guidance law for formation flight, the virtual structure approach is used. To develop a guidance law for collision avoidance considering both other UAVs and unknown static obstacles, a geometric approach using information such as a relative position vector is utilized. Through the Lyapunov theorem, the stability of the proposed guidance law is proved. To combine guidance commands, the concept of the elastic weighting factor inspired by the elastic behavior of shape memory polymer, which tends to regain its original shape after deformation, is introduced. By using the concept of elastic weighting factor, multiple UAVs are able to cope actively with the situation of a collision between both UAVs and static obstacles during the formation flight. To verify the performance of the proposed method, numerical simulations are performed.

Self-Recurrent Wavelet Neural Network Based Direct Adaptive Control for Stable Path Tracking of Mobile Robots

  • You, Sung-Jin;Oh, Joon-Seop;Park, Jin-Bae;Choi, Yoon-Ho
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2004년도 ICCAS
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    • pp.640-645
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    • 2004
  • This paper proposes a direct adaptive control method using self-recurrent wavelet neural network (SRWNN) for stable path tracking of mobile robots. The architecture of the SRWNN is a modified model of the wavelet neural network (WNN). Unlike the WNN, since a mother wavelet layer of the SRWNN is composed of self-feedback neurons, the SRWNN has the ability to store the past information of the wavelet. For this ability of the SRWNN, the SRWNN is used as a controller with simpler structure than the WNN in our on-line control process. The gradient-descent method with adaptive learning rates (ALR) is applied to train the parameters of the SRWNN. The ALR are derived from discrete Lyapunov stability theorem, which are used to guarantee the stable path tracking of mobile robots. Finally, through computer simulations, we demonstrate the effectiveness and stability of the proposed controller.

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컨베이어 추적을 위한 로보트 팔의 강인한 적응 제어계 설계 (A Design of Robust Adaptive Control Systems of Robot Arms for conveyor Tracking)

  • 엄기환;손동설;김주홍
    • 한국통신학회논문지
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    • 제15권11호
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    • pp.945-954
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    • 1990
  • 로보트 팔이 컨베이어를 추적하는 강인한 적응제어계를 작업좌표에서 설계하였다. 제안한 설계방식은 모델규범형 설계방식과 Popov의 초안정정리를 기본으로 하였고 보조입력을 사용하여 Lyapunov 함수 V(t)와 시간미분 V와의 比의 크기를 크게하여 속응성을 좋게하여 과도특성을 개선하였다. 설계변수{lambda} 와 하중함수 $L_K$에서 $L_K$의 값이 {lambda}의 값보다 작은 경우에는 계통이 안정하나 $L_K$의 값이 {lambda}의 값보다 큰 경우에는 계통이 불안정하였다.

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유연 관절 로봇의 적응 고장 수용 제어 (Adaptive Fault Accommodation Control for Flexible-Joint Robots)

  • 유성진
    • 한국지능시스템학회논문지
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    • 제23권1호
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    • pp.46-50
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    • 2013
  • 본 논문은 다수의 구동기 고장을 가진 유연 관절 로봇의 적응 고장 수용 제어기를 제안한다. 다수의 구동기 고장의 크기와 일어나는 시간은 알려지지 않는다고 가정한다. 구동기 고장을 수용하기 위해 추종 오차의 수렴율과 오버슈트의 최대치로 특성화된 미리 정의된 성능을 보장하는 유계 조건을 갖는 적응 고장 수용 제어기를 설계한다. 르아프노브 안정도 이론을 이용하여 페루트 시스템의 모든 신호가 준 전역적이고 균일하고 궁극적으로 유계됨을 증명하고 추종 오차가 미리 정의된 성능 유계에서 벗어나지 않음을 보인다.

적응제어형 외란 관측기를 이요한 BLDC 전동기의 정밀위치제어에 대한 연구 (A Study on Adaptive Load Torque Observer for Robust Precision Position Control of BLDC Motor)

  • 고종선;윤성구
    • 전력전자학회:학술대회논문집
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    • 전력전자학회 1999년도 전력전자학술대회 논문집
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    • pp.4-9
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    • 1999
  • A new control method for precision robust position control of a brushless DC (BLDC) motor using asymptotically stable adaptive load torque observer is presented in the paper. Precision position control is obtained for the BLDC motor system approximately linearized using the field-orientation method Recently, many of these drive systems use BLDC motors to avoid backlashe. However, the disadvantages of the motor are high cost and complex control because of nonlinear characteristics. Also, the load torque disturbance directly affects the motor shaft. The application of the load torque observer is published in [1] using fixed gain. However, the motor flux linkage is not exactly known for a load torque observer. There is the problem of uncertainty to obtain very high precision position control. Therefore a model reference adaptive observer is considered to overcome the problem of unknown parameter and torque disturbance in this paper. The system stability analysis is carried out using Lyapunov stability theorem. As a result, asymptotically stable observe gain can be obtained without affecting the overall system response. The load disturbance detected by the asymptotically stable adaptive observer is compensated by feedforwarding the equivalent current which gives fast response. The experimenta results are presented in the paper.

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Stabilizing Control of DC/DC Buck Converters with Constant Power Loads in Continuous Conduction and Discontinuous Conduction Modes Using Digital Power Alignment Technique

  • Khaligh Alireza;Emadi Ali
    • Journal of Electrical Engineering and Technology
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    • 제1권1호
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    • pp.63-72
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    • 2006
  • The purpose of this raper is to address the negative impedance instability in DC/DC converters. We present the negative impedance instability of PWM DC/DC converters loaded by constant power loads (CPLs). An approach to design digital controllers for DC/DC converters Is presented. The proposed method, called Power Alignment control technique, is applied to DC/DC step-down choppers operating in continuous conduction or discontinuous conduction modes with CPLs. This approach uses two predefined state variables instead of conventional pulse width modulation (PWM) to regulate the output voltage. A comparator compares actual output voltage with the reference and then switches between the appropriate states. It needs few logic gates and comparators to be implemented thus, making it extremely simple and easy to develop using a low-cost application specific integrated circuit (ASIC) for converters with CPLs. Furthermore, stability of the proposed controllers using the small signal analysis as well as the second theorem of Lyapunov is verified. Finally, simulation and analytical results are presented to describe and verify the proposed technique.

A Backstepping Control of LSM Drive Systems Using Adaptive Modified Recurrent Laguerre OPNNUO

  • Lin, Chih-Hong
    • Journal of Power Electronics
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    • 제16권2호
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    • pp.598-609
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    • 2016
  • The good control performance of permanent magnet linear synchronous motor (LSM) drive systems is difficult to achieve using linear controllers because of uncertainty effects, such as fictitious forces. A backstepping control system using adaptive modified recurrent Laguerre orthogonal polynomial neural network uncertainty observer (OPNNUO) is proposed to increase the robustness of LSM drive systems. First, a field-oriented mechanism is applied to formulate a dynamic equation for an LSM drive system. Second, a backstepping approach is proposed to control the motion of the LSM drive system. With the proposed backstepping control system, the mover position of the LSM drive achieves good transient control performance and robustness. As the LSM drive system is prone to nonlinear and time-varying uncertainties, an adaptive modified recurrent Laguerre OPNNUO is proposed to estimate lumped uncertainties and thereby enhance the robustness of the LSM drive system. The on-line parameter training methodology of the modified recurrent Laguerre OPNN is based on the Lyapunov stability theorem. Furthermore, two optimal learning rates of the modified recurrent Laguerre OPNN are derived to accelerate parameter convergence. Finally, the effectiveness of the proposed control system is verified by experimental results.