• Title/Summary/Keyword: Lyapunov stability theorem

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A Novel Robust Adaptive Control Algorithm for Systems with Unknown Disturbances (미지의 외란을 가지는 시스템의 새로운 형태의 적응 제어 알고리즘)

  • Koo, Keun-Mo;Jeon, Jeong-Yeol;Kim, Jong-Hwan
    • Proceedings of the KIEE Conference
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    • 1992.07a
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    • pp.371-373
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    • 1992
  • This note proposes a novel robust adaptive control algorithm for systems with unknown disturbances by introducing an additional term in the control input. This additional term is easily implementable by estimating the upper bound of the unknown disturbances. By this term, the output error can be made to be uniformly ultimately bounded in a desired region via Lyapunov second stability theorem when the relative degree of system is one.

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Chattering-Free Sliding Mode Control with a Time-Varying Sliding Surface

  • Kyung, Tai-Hyun;Kim, Jong-Shik;Lee, Kyu-Joon
    • 제어로봇시스템학회:학술대회논문집
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    • 2001.10a
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    • pp.151.4-151
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    • 2001
  • Chattering-free sliding mode control is derived from the reaching law method and Lyapunov stability theorem. Its control input Is composed of continuous term and discontinuous term. By the combination of these terms, the robustness and tracking performance can be improved and the chattering can be avoided. But in the reaching mode, the sliding mode control is sensitive to the modeling uncertainties, parameter variations and disturbances, also it needs a large control input. These result in poor transient responses. In this paper, to overcome these problems in the reaching mode, a time-varying sliding surface is proposed. And it is applied to a 2-link SCARA robot manipulator, experimental results show that the transient response is improved and its ...

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Robust Adaptive Control of A HexaSlide Type Parallel Manipulator

  • Kim, Jong-Phil;Kim, Sung-Gaun;Ryu, Jeha
    • Transactions on Control, Automation and Systems Engineering
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    • v.3 no.4
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    • pp.262-267
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    • 2001
  • Jeha Ryu Department of Mechatronics, Kwangju Institute of Science and Technology This paper presents an application of a robust adaptive control strategy to HexaSlide type six degrees-of-freedom parallel manipulators. The HexaSlide type parallel manipulators are characterized as an architecture with constant link lengths that are attached to moving sliders on the ground and to a mobile platform. The proposed control law is developed based on a simplified second order system dynamic equation in joint space with uncertain mass, damper, spring, and Coulomb friction terms. These uncertain parameters are updated by an adaptation law that is derived by Lyapunov stability theorem. A robust adaptive control law by using the boundary layer is designed for the purpose of compensating for the neglected dynamic effects of the mobile platform and the six moving links that are modeled as a disturbance term. Experimental results show good and fast tracking performance.

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Research on Fuzzy I-PD Optimal Preview Control

  • Wang, Dong;Aida, Kazuo
    • 제어로봇시스템학회:학술대회논문집
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    • 2000.10a
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    • pp.483-483
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    • 2000
  • The Fuzzy Preview Control (FPC) design methodology using I-PD Preview Control (IPC) and Optimal Preview Control (OPC)[6] are discussed in this paper. First we show a new fuzzy controller with single input single output, and build a relationship between it and the I-PD Control proposed by Kitamari, as well as Optimal Control with some specific equations. We also give the stability analysis with Lyapunov theorem. On this way, we can design a Fuzzy I-PD Controller (FIC) very easier and more effective. Then, preview control element design methodology of FCP was given according to IPC and OPC. Third, to make the system more rapidly and more little overshooting, two factors are given to adjust the controller's properties. At last, the performance of FPC is revealed via computer simulation using a nonlinear plant.

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A Adaptive Scheme design for Identification and Control of multivariable Systems (다변수시스템의 상태식별과 제어를 위한 안정한 적응구조의 설계)

  • Kim, S.K.;Chun, S.Y.;Yim, W.Y.
    • Proceedings of the KIEE Conference
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    • 1987.11a
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    • pp.69-72
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    • 1987
  • General schemes for the adaptive control and identification of multivariable systems by model reference approach are developed. Lyapunov's direct method and LaSalle's theorem are employed to ensure the stability of these schemes. An added feature is the simplicity of the stable adaptive laws, which depend explicitly on the state variables of plant and model, and on the plant input. Computer simulation results of several examples illustrate the the effectiveness of the proposed schemes.

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Wavelet Neural Network Controller for AQM in a TCP Network: Adaptive Learning Rates Approach

  • Kim, Jae-Man;Park, Jin-Bae;Choi, Yoon-Ho
    • International Journal of Control, Automation, and Systems
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    • v.6 no.4
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    • pp.526-533
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    • 2008
  • We propose a wavelet neural network (WNN) control method for active queue management (AQM) in an end-to-end TCP network, which is trained by adaptive learning rates (ALRs). In the TCP network, AQM is important to regulate the queue length by passing or dropping the packets at the intermediate routers. RED, PI, and PID algorithms have been used for AQM. But these algorithms show weaknesses in the detection and control of congestion under dynamically changing network situations. In our method, the WNN controller using ALRs is designed to overcome these problems. It adaptively controls the dropping probability of the packets and is trained by gradient-descent algorithm. We apply Lyapunov theorem to verify the stability of the WNN controller using ALRs. Simulations are carried out to demonstrate the effectiveness of the proposed method.

Stable Predictive Control of Chaotic Systems Using Self-Recurrent Wavelet Neural Network

  • Yoo Sung Jin;Park Jin Bae;Choi Yoon Ho
    • International Journal of Control, Automation, and Systems
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    • v.3 no.1
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    • pp.43-55
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    • 2005
  • In this paper, a predictive control method using self-recurrent wavelet neural network (SRWNN) is proposed for chaotic systems. Since the SRWNN has a self-recurrent mother wavelet layer, it can well attract the complex nonlinear system though the SRWNN has less mother wavelet nodes than the wavelet neural network (WNN). Thus, the SRWNN is used as a model predictor for predicting the dynamic property of chaotic systems. The gradient descent method with the adaptive learning rates is applied to train the parameters of the SRWNN based predictor and controller. The adaptive learning rates are derived from the discrete Lyapunov stability theorem, which are used to guarantee the convergence of the predictive controller. Finally, the chaotic systems are provided to demonstrate the effectiveness of the proposed control strategy.

Adaptive Formation Control of Nonholonomic Multiple Mobile Robots Considering Unknown Slippage (미지의 미끄러짐을 고려한 비홀로노믹 다개체 이동 로봇의 적응 군집 제어)

  • Choi, Yoon-Ho;Yoo, Sung-Jin
    • Journal of Institute of Control, Robotics and Systems
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    • v.16 no.1
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    • pp.5-11
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    • 2010
  • An adaptive formation control approach is proposed for nonhonolomic multiple mobile robots considering unknown slipping and skidding. It is assumed that unknown slipping and skidding effects are bounded by unknown constants. Under this assumption, the adaptive technique is employed to estimate the bounds of unknown slipping and skidding effects of each mobile robot. To deal with the skidding effect included in kinematics, the dynamic surface design approach is applied to design a local controller for each mobile robot. Using Lyapunov stability theorem, the adaptation laws for tuning bounds of slipping and skidding are induced and it is proved that all signals of the closed-loop system are bounded and the tracking errors and the synchronization errors of the path parameters converge to an adjustable neighborhood of the origin. Finally, simulation results are provided to verify the effectiveness of the proposed approach.

Adaptive Neural Dynamic Surface Control via H Approach for Nonlinear Flight Systems (비선형 비행 시스템을 위한 H 접근법 기반 적응 신경망 동적 표면 제어)

  • Yoo, Sung-Jin;Choi, Yoon-Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.14 no.3
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    • pp.254-262
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    • 2008
  • In this paper, we propose an adaptive neural dynamic surface control (DSC) approach with $H_{\infty}$ tracking performance for full dynamics of nonlinear flight systems. It is assumed that the model uncertainties such as structured and unstrutured uncertainties, and external disturbances influence the nonlinear aircraft model. In our control system, self recurrent wavelet neural networks (SRWNNs) are used to compensate the model uncertainties of nonlinear flight systems, and an adaptive DSC technique is extended for the disturbance attenuation of nonlinear flight systems. All weights of SRWNNs are trained on-line by the smooth projection algorithm. From Lyapunov stability theorem, it is shown that $H_{\infty}$ performance nom external disturbances can be obtained. Finally, we present the simulation results for a nonlinear six-degree-of-freedom F-16 aircraft model to confirm the effectiveness of the proposed control system.

A Study on the Adaptive Roll Control Scheme for the Top Attack Smart Projectile (상부공격 지능탄의 회전각 적응제어 기법 연구)

  • 홍종태;정수경;최상경
    • Journal of the Korea Institute of Military Science and Technology
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    • v.3 no.2
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    • pp.61-70
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    • 2000
  • An Adaptive Positive Position Feedback method is presented for controlling the roll of the supersonic smart projectile. The proposed strategy combines the attractive attributes of Positive Position Feedback(PPF) of Goh and Caughey, and Lyapunov stability theorem. The parameters of Adaptive-PFF controller are adjusted in an adaptive mauler in order to follow the performance of an optimal reference model. In this way, optimal damping and zero steady-state errors can be achieved even in the presence of uncertain or changing plant parameters. The performance obtained with the Adaptive-PPF algorithm is compared with conventional PPF control algorithm. The results obtained emphasize the potential of Adaptive-PPF algorithm as an efficient means for controlling plants such as supersonic flight systems with uncertainties in real time.

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