• Title/Summary/Keyword: control Lyapunov function

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Robust Adaptive Controller for MIMO Nonsquare Nonlinear Systems Using Universal Function Approximators

  • Park, Jang-Hyun;Seo, Ho-Joon;Park, Gwi-Tae
    • 제어로봇시스템학회:학술대회논문집
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    • 2001.10a
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    • pp.40.4-40
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    • 2001
  • This paper addresses the problem of designing robust adaptive output tracking control for a class of MIMO nonlinear systems which have different number of inputs and outputs The stability of the whole closed-loop system is guaranteed in the sense of Lyapunov and uniformly Itimately boundedness of the tracking error vector as well as estimated parameters are shown. In addition, we show that the restrictive assumptions on input gain matrix which is presumed in the past works can be eliminated by using proposed control law.

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Modeling and designing intelligent adaptive sliding mode controller for an Eight-Rotor MAV

  • Chen, Xiang-Jian;Li, Di
    • International Journal of Aeronautical and Space Sciences
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    • v.14 no.2
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    • pp.172-182
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    • 2013
  • This paper focuses on the modeling and intelligent control of the new Eight-Rotor MAV, which is used to solve the problem of the low coefficient proportion between lift and gravity for the Quadrotor MAV. The Eight-Rotor MAV is a nonlinear plant, so that it is difficult to obtain stable control, due to uncertainties. The purpose of this paper is to propose a robust, stable attitude control strategy for the Eight-Rotor MAV, to accommodate system uncertainties, variations, and external disturbances. First, an interval type-II fuzzy neural network is employed to approximate the nonlinearity function and uncertainty functions in the dynamic model of the Eight-Rotor MAV. Then, the parameters of the interval type-II fuzzy neural network and gain of sliding mode control can be tuned on-line by adaptive laws based on the Lyapunov synthesis approach, and the Lyapunov stability theorem has been used to testify the asymptotic stability of the closed-loop system. The validity of the proposed control method has been verified in the Eight-Rotor MAV through real-time experiments. The experimental results show that the performance of the interval type-II fuzzy neural network based adaptive sliding mode controller could guarantee the Eight-Rotor MAV control system good performances under uncertainties, variations, and external disturbances. This controller is significantly improved, compared with the conventional adaptive sliding mode controller, and the type-I fuzzy neural network based sliding mode controller.

The Sliding Controller designed by the Indirect Adaptive Fuzzy Control Method (간접 적응 퍼지 제어기법에 의한 슬라이딩 제어기 설계)

  • Choi, Chang-Ho;Yim, Wha-Yeong
    • Proceedings of the KIEE Conference
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    • 2000.07d
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    • pp.2283-2286
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    • 2000
  • Sliding control is a powerful approach to controlling nonlinear and uncertain systems. Conventional sliding mode control suffer' from high control gain and chattering problem. also it needs mathematic! modeling equations for control systems. A Fuzzy controller is endowed with control rules and membership function that are constructed on the knowledge of expert, as like intuition and experience. but It is very difficult to obtain the exact values which are the membership function and consequent parameters. In this paper, without mathematical modeling equations, the plant parameters in sliding mode are estimated by the indirect adaptive fuzzy method. the proposed algorithm could analyze the system's stability and convergence behavior using Lyapunov theory. so sliding modes are reconstructed and decreased tracking error. moreover convergence time took a short. An example of inverted pendulum is given for demonstration of the robustness of proposed methodology.

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Complexity Control Method of Chaos Dynamics in Recurrent Neural Networks

  • Sakai, Masao;Homma, Noriyasu;Abe, Kenichi
    • Transactions on Control, Automation and Systems Engineering
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    • v.4 no.2
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    • pp.124-129
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    • 2002
  • This paper demonstrates that the largest Lyapunov exponent λ of recurrent neural networks can be controlled efficiently by a stochastic gradient method. An essential core of the proposed method is a novel stochastic approximate formulation of the Lyapunov exponent λ as a function of the network parameters such as connection weights and thresholds of neural activation functions. By a gradient method, a direct calculation to minimize a square error (λ - λ$\^$obj/)$^2$, where λ$\^$obj/ is a desired exponent value, needs gradients collection through time which are given by a recursive calculation from past to present values. The collection is computationally expensive and causes unstable control of the exponent for networks with chaotic dynamics because of chaotic instability. The stochastic formulation derived in this paper gives us an approximation of the gradients collection in a fashion without the recursive calculation. This approximation can realize not only a faster calculation of the gradient, but also stable control for chaotic dynamics. Due to the non-recursive calculation. without respect to the time evolutions, the running times of this approximation grow only about as N$^2$ compared to as N$\^$5/T that is of the direct calculation method. It is also shown by simulation studies that the approximation is a robust formulation for the network size and that proposed method can control the chaos dynamics in recurrent neural networks efficiently.

Tracking Control for Robot Manipulators based on Radial Basis Function Networks

  • Lee, Min-Jung;Park, Jin-Hyun;Jun, Hyang-Sig;Gahng, Myoung-Ho;Choi, Young-Kiu
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • v.9 no.1
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    • pp.285-288
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    • 2005
  • Neural networks are known as kinds of intelligent strategies since they have learning capability. There are various their applications from intelligent control fields; however, their applications have limits from the point that the stability of the intelligent control systems is not usually guaranteed. In this paper we propose a neuro-adaptive controller for robot manipulators using the radial basis function network(RBFN) that is a kind of a neural network. Adaptation laws for parameters of the RBFN are developed based on the Lyapunov stability theory to guarantee the stability of the overall control scheme. Filtered tracking errors between the actual outputs and desired outputs are discussed in the sense of the uniformly ultimately boundedness(UUB). Additionally, it is also shown that the parameters of the RBFN are bounded. Experimental results for a SCARA-type robot manipulator show that the proposed neuro-adaptive controller is adaptable to the environment changes and is more robust than the conventional PID controller and the neuro-controller based on the multilayer perceptron.

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

  • ;Ye-Hwa, Chen
    • 제어로봇시스템학회:학술대회논문집
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    • 1993.10a
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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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Adaptive Fuzzy Control of Helicopter (헬리콥터의 적응 퍼지제어)

  • Jin, Zong-Hua;Jang, Yong-Jool;Lee, Won-Chang;Kang, Geun-Taek
    • Journal of the Korean Institute of Intelligent Systems
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    • v.13 no.5
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    • pp.564-570
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    • 2003
  • This paper presents an adaptive fuzzy control scheme for nonlinear helicopter system which has uncertainty or unknown variations in parameters. The proposed adaptive fuzzy controller is a model reference adaptive controller. The parameters of fuzzy controller are adjusted so that the plant output tracks the reference model output. It is shown that the adaptive law guarantees the stability of the closed-loop system by using Lyapunov function. Several experiments with a small model helicopter having parameter variations are performed to show the usefulness of the proposed adaptive fuzzy controller.

Fuzzy-Sliding-Sector Control for Chattering Reduction (채터링 감소를 위한 퍼지 슬라이딩 섹터 제어)

  • Han, Jong-Kil;Son, Yong-Su
    • The Journal of the Korea institute of electronic communication sciences
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    • v.4 no.3
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    • pp.211-216
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    • 2009
  • Chattering phenomenon is still a large drawback of VSS. To overcome this problem, various approaches have been reported. A new notion of sliding sector has been proposed recently. In this paper, fuzzy control with time-varying boundary layer using the sliding sector theory with continued input function in the sector is proposed. This paper analyzes the stability, using Lyapunov function on the sliding sector. Computer simulation for inverted pendulum results in elimination of the chattering phenomenon.

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

  • Kim, Youngjoo;Bang, Hyochoong
    • Journal of Institute of Control, Robotics and Systems
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    • v.22 no.9
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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.

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

  • Han, Jong-Kil;Son, Yong-Su
    • The Journal of the Korea institute of electronic communication sciences
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    • v.2 no.3
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    • pp.168-173
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    • 2007
  • Chattering phenomenon is still a large drawback of VSS. To overcome this problem, various approaches have been reported. A new notion of sliding sector has been proposed recently. In this paper, new methods of the nonlinear system control using the sliding sector theory with continued input function in the sector is proposed. This paper analyzes the stability, using Lyapunov function on the sliding sector. computer simulation for inverted pendulum results in elimination of the chattering phenomenon.

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