• 제목/요약/키워드: Lyapunov Function

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Nonlinear Observer flay Applications of Fermentation Process in Stirred Tank Bioreactor

  • Kim, Hak-Kyeong;Nguyen, Tan-Tien;Kim, Sang-Bong
    • Transactions on Control, Automation and Systems Engineering
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    • 제4권3호
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    • pp.244-250
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    • 2002
  • This paper proposed a modified observer based on Busawon's high gain observer using an appropriate time depended function, which can be chosen to make each estimated state converge faster to its real value. The stability of the modified observer is proved by using Lyapunov function. The modified nonlinear observer is applied to estimate the states in stirred tank bioreactor: out-put substrate concentration, output biomass concentration and the specific growth rate of the process. The convergences of the modified observer and Busawon's observer are compared trough simulation results. As the results, the modified observer converges faster to its real value than the well-known Busawon's observer.

표적 추적 성능 최적화 및 충돌 회피를 위한 다수 에이전트 분산 제어 (Decentralized Control of Multiple Agents for Optimizing Target Tracking Performance and Collision Avoidance)

  • 김영주;방효충
    • 제어로봇시스템학회논문지
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    • 제22권9호
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    • pp.693-698
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    • 2016
  • A decentralized control method is proposed to enable a group of robots to achieve maximum performance in multisensory target tracking while avoiding collision with the target. The decentralized control was designed based on navigation function formalism. The study showed that the multiple agent system converged to the positions providing the maximum performance by the decentralized controller, based on Lyapunov and Hessian theory. An exemplary simulation was given for a multiple agent system tracking a stationary target.

채터링 감소를 위한 슬라이딩 섹터를 갖은 슬라이딩 제어 (Sliding Mode Control with Sliding Sector for Chattering Reduction)

  • 한종길;손영수
    • 한국전자통신학회논문지
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    • 제2권3호
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    • pp.168-173
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    • 2007
  • 채터링 현상은 VSS의 주요한 약점이며 이 문제를 극복하기위하여 많은 연구들이 발표되었다. 선형 슬라이딩 섹터 이론이 최근에 발표되었으며, 본 논문에서는 섹터 내부에 연속입력함수를 가진 슬라이딩 섹터이론을 이용하여 비선형시스템 제어하는 새로운 방식을 제안하고, 슬라이딩 섹터에 리아프노프 함수를 이용하여 안정도를 분석한다. 역진자 시스템에 컴퓨터 시뮬레이션을 통하여 채터링 현상의 제거를 확인한다.

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ON THE LEBESGUE SPACE OF VECTOR MEASURES

  • Choi, Chang-Sun;Lee, Keun-Young
    • 대한수학회보
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    • 제48권4호
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    • pp.779-789
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    • 2011
  • In this paper we study the Banach space $L^1$(G) of real valued measurable functions which are integrable with respect to a vector measure G in the sense of D. R. Lewis. First, we investigate conditions for a scalarly integrable function f which guarantee $f{\in}L^1$(G). Next, we give a sufficient condition for a sequence to converge in $L^1$(G). Moreover, for two vector measures F and G with values in the same Banach space, when F can be written as the integral of a function $f{\in}L^1$(G), we show that certain properties of G are inherited to F; for instance, relative compactness or convexity of the range of vector measure. Finally, we give some examples of $L^1$(G) related to the approximation property.

비선형 시스템의 동정을 위한 안정한 웨이블릿 기반 퍼지 뉴럴 네트워크 (Stable Wavelet Based Fuzzy Neural Network for the Identification of Nonlinear Systems)

  • 오준섭;박진배;최윤호
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2005년도 제36회 하계학술대회 논문집 D
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    • pp.2681-2683
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    • 2005
  • In this paper, we present the structure of fuzzy neural network(FNN) based on wavelet function, and apply this network structure to the identification of nonlinear systems. For adjusting the shape of membership function and the connection weights, the parameter learning method based on the gradient descent scheme is adopted. And an approach that uses adaptive learning rates is driven via a Lyapunov stability analysis to guarantee the fast convergence. Finally, to verify the efficiency of our network structure. we compare the Identification performance of proposed wavelet based fuzzy neural network(WFNN) with those of the FNN, the wavelet fuzzy model(WFM) and the wavelet neural network(WNN) through the computer simulation.

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로봇 매니퓰레이터의 새로운 견실제어기 설계 (New Robust Control Fesigns of Robot Manipulators)

  • 한명철
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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    • pp.666-671
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    • 1993
  • A new robust control law is proposed for uncertain rigid robots and two composite robust control laws for flexible-joint manipulators which contain uncertainties. The uncertainty, is nonlinear and (possibly fast) time-varying. Therefore, the uncertain factors such as imperfect modeling, function, payload change, and external disturbances are all addressed. Based only on the possible bound of the uncertainty, a robust controller is constructed for the rigid counterpart of the flexible-joint robot Some feedback control terms are then added to the robust control law to stabilize the elastic vibrations at the joints. To show that the proposed composite robust control laws are indeed applicable to flexible-joint robots, a singular perturbation approach and the stability study based on Lyapunov function are proposed.

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Smooth Formation Navigation of Multiple Mobile Robots for Avoiding Moving Obstacles

  • Chen Xin;Li Yangmin
    • International Journal of Control, Automation, and Systems
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    • 제4권4호
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    • pp.466-479
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    • 2006
  • This paper addresses a formation navigation issue for a group of mobile robots passing through an environment with either static or moving obstacles meanwhile keeping a fixed formation shape. Based on Lyapunov function and graph theory, a NN formation control is proposed, which guarantees to maintain a formation if the formation pattern is $C^k,\;k\geq1$. In the process of navigation, the leader can generate a proper trajectory to lead formation and avoid moving obstacles according to the obtained information. An evolutionary computational technique using particle swarm optimization (PSO) is proposed for motion planning so that the formation is kept as $C^1$ function. The simulation results demonstrate that this algorithm is effective and the experimental studies validate the formation ability of the multiple mobile robots system.

Nonlinear Adaptive Control of Fermentation Process in Stirred Tank Bioreactor

  • Kim, Sang-Bong;Kim, Hak-Kyeong;Soo, Jeong-Nam;Nguyen, Tan-Tien
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2001년도 ICCAS
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    • pp.74.3-74
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    • 2001
  • This paper proposes a nonlinear adaptive controller based on back-stepping method for tracking reference substrate concentration by manipulating dilution rate in a continuous baker´s yeast cultivating process in stirred tank bioreactor. Control law is obtained from Lyapunov control function to ensure asymptotical stability of the system. The Haldane model for the specific growth rate depending on only substrate concentration is used in this paper. Due to the uncertainty of specific growth rate, it has been modified as a function including the unknown parameter with known bounded values. The substrate concentration in the bioreactor and feed line are measured. The deviation from the reference is observed when the external disturbance such as the change of the feed is introduced to the system ...

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Nonlinear Adaptive Control of Fermentation Process in Stirred Tank Bioreactor

  • Kim, Hak-Kyeong;Nguyen, Tan-Tien;Nam soo Jeong;Kim, Sang-Bong
    • Transactions on Control, Automation and Systems Engineering
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    • 제4권4호
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    • pp.277-282
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    • 2002
  • This paper proposes a nonlinear adaptive controller based on back-stepping method for tracking reference substrate concentration by manipulating dilution rate in a continuous baker's yeast cultivating process in stirred tank bioreactor. Control law is obtained from Lyapunov control function to ensure asymptotical stability of the system. The Haldane model for the specific growth rate depending on only substrate concentration is used in this paper. Due to the uncertainty of specific growth rate, it has been modified as a function including the unknown parameter with known bounded values. The substrate concentration in the bioreactor and feed line are measured. The deviation from the reference is observed when the external disturbance such as the change of the feed is introduced to the system. The effectiveness of the proposed controller is shown through simulation results in continuous system.

간편 간접추론 퍼지논리 경계층을 갖는 슬라이딩 모드 제어기의 설계 (Design of Sliding Mode Controller with a SIIM Fuzzy Logic Boundary Layer)

  • 채창현
    • 전자공학회논문지SC
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    • 제41권2호
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    • pp.45-52
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    • 2004
  • 본 논문에서는 슬라이딩 라인 함수의 각 요소를 간편 간접추론 퍼지 논리의 입력변수로 사용하여 슬라이딩 모드 제어기의 경계층을 모사하는 간편 간접추론 퍼지논리 경계층을 갖는 슬라이딩 모드 제어기를 설계하였다. 제안된 제어시스템은 별도의 비선형 함수를 구할 필요가 없으며, 네 개의 퍼지규칙으로 이루어지므로 간단하고 안정도 증명이 쉬운 장점을 가진다. 본 논문의 유효성을 비선형 시변 시스템에 적용하여 고찰하였다.