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Observed-based adaptive neural tracking control for nonlinear systems with unknown control directions and input delay
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作者 DENG Yuxuan WANG Qingling 《Journal of Systems Engineering and Electronics》 2025年第1期269-279,共11页
Enhancing the stability and performance of practical control systems in the presence of nonlinearity,time delay,and uncertainty remains a significant challenge.Particularly,a class of strict-feedback nonlinear uncerta... Enhancing the stability and performance of practical control systems in the presence of nonlinearity,time delay,and uncertainty remains a significant challenge.Particularly,a class of strict-feedback nonlinear uncertain systems characterized by unknown control directions and time-varying input delay lacks comprehensive solutions.In this paper,we propose an observerbased adaptive tracking controller to address this gap.Neural networks are utilized to handle uncertainty,and a unique coordinate transformation is employed to untangle the coupling between input delay and unknown control directions.Subsequently,a new auxiliary signal counters the impact of time-varying input delay,while a Nussbaum function is introduced to solve the problem of unknown control directions.The leverage of an advanced dynamic surface control technique avoids the“complexity explosion”and reduces boundary layer errors.Synthesizing these techniques ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded(SGUUB),and the tracking error converges to a small region around the origin by selecting suitable parameters.Simulation examples are provided to demonstrate the feasibility of the proposed approach. 展开更多
关键词 adaptive neural network dynamic surface control unknown control direction input delay
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A Fractional-Order Ultra-Local Model-Based Adaptive Neural Network Sliding Mode Control of n-DOF Upper-Limb Exoskeleton With Input Deadzone
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作者 Dingxin He HaoPing Wang +1 位作者 Yang Tian Yida Guo 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第3期760-781,共22页
This paper proposes an adaptive neural network sliding mode control based on fractional-order ultra-local model for n-DOF upper-limb exoskeleton in presence of uncertainties,external disturbances and input deadzone.Co... This paper proposes an adaptive neural network sliding mode control based on fractional-order ultra-local model for n-DOF upper-limb exoskeleton in presence of uncertainties,external disturbances and input deadzone.Considering the model complexity and input deadzone,a fractional-order ultra-local model is proposed to formulate the original dynamic system for simple controller design.Firstly,the control gain of ultra-local model is considered as a constant.The fractional-order sliding mode technique is designed to stabilize the closed-loop system,while fractional-order time-delay estimation is combined with neural network to estimate the lumped disturbance.Correspondingly,a fractional-order ultra-local model-based neural network sliding mode controller(FO-NNSMC) is proposed.Secondly,to avoid disadvantageous effect of improper gain selection on the control performance,the control gain of ultra-local model is considered as an unknown parameter.Then,the Nussbaum technique is introduced into the FO-NNSMC to deal with the stability problem with unknown gain.Correspondingly,a fractional-order ultra-local model-based adaptive neural network sliding mode controller(FO-ANNSMC) is proposed.Moreover,the stability analysis of the closed-loop system with the proposed method is presented by using the Lyapunov theory.Finally,with the co-simulations on virtual prototype of 7-DOF iReHave upper-limb exoskeleton and experiments on 2-DOF upper-limb exoskeleton,the obtained compared results illustrate the effectiveness and superiority of the proposed method. 展开更多
关键词 adaptive control input deadzone model-free control n-DOF upper-limb exoskeleton neural network
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ADAPTIVE NEURAL NETWORK ATTITUDE CONTROL FOR UNMANNED HELICOPTER
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作者 王辉 徐锦法 高正 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2004年第3期168-173,共6页
Adaptive flight control technology, feedback linearization, model inversion theory are reviewed and the error dynamic characteristics are analyzed, and an adaptive on-line neural network attitude control system is pre... Adaptive flight control technology, feedback linearization, model inversion theory are reviewed and the error dynamic characteristics are analyzed, and an adaptive on-line neural network attitude control system is presented. The model inversion is under the hover condition. And the adaptive control law based on the neural network is designed to guarantee the boundedness of tracking error and control signals. Simulation results demonstrate that the nonlinear neural network augmented model inversion can self-adapt to the uncertainty and modeling errors of unmanned helicopters. Results are compared while the parameters of PD controller and robustness items are changed. 展开更多
关键词 neural network adaptive control unmanned helicopter flight control
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Adaptive Control Based on Neural Networks for an Uncertain 2-DOF Helicopter System With Input Deadzone and Output Constraints 被引量:15
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作者 Yuncheng Ouyang Lu Dong +1 位作者 Lei Xue Changyin Sun 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2019年第3期807-815,共9页
In this paper, a study of control for an uncertain2-degree of freedom(DOF) helicopter system is given. The2-DOF helicopter is subject to input deadzone and output constraints. In order to cope with system uncertaintie... In this paper, a study of control for an uncertain2-degree of freedom(DOF) helicopter system is given. The2-DOF helicopter is subject to input deadzone and output constraints. In order to cope with system uncertainties and input deadzone, the neural network technique is introduced because of its capability in approximation. In order to update the weights of the neural network, an adaptive control method is utilized to improve the system adaptability. Furthermore, the integral barrier Lyapunov function(IBLF) is adopt in control design to guarantee the condition of output constraints and boundedness of the corresponding tracking errors. The Lyapunov direct method is applied in the control design to analyze system stability and convergence. Finally, numerical simulations are conducted to prove the feasibility and effectiveness of the proposed control based on the model of Quanser's 2-DOF helicopter. 展开更多
关键词 2-degree of FREEDOM (DOF) helicopter adaptive control INPUT DEADZONE integral barrier Lyapunov function neural networks output constraints
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Neural Network-Based Adaptive Motion Control for a Mobile Robot with Unknown Longitudinal Slipping 被引量:8
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作者 Gang Wang Xiaoping Liu +1 位作者 Yunlong Zhao Song Han 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2019年第4期26-34,共9页
When the mobile robot performs certain motion tasks in complex environment, wheel slipping inevitably occurs due to the wet or icy road and other reasons, thus directly influences the motion control accuracy. To addre... When the mobile robot performs certain motion tasks in complex environment, wheel slipping inevitably occurs due to the wet or icy road and other reasons, thus directly influences the motion control accuracy. To address unknown wheel longitudinal slipping problem for mobile robot, a RBF neural network approach based on whole model approximation is presented. The real-time data acquisition of inertial measure unit(IMU), encoders and other sensors is employed to get the mobile robot’s position and orientation in the movement, which is applied to compensate the unknown bounds of the longitudinal slipping using the adaptive technique. Both the simulation and experimental results prove that the control scheme possesses good practical performance and realize the motion control with unknown longitudinal slipping. 展开更多
关键词 Mobile robot Longitudinal slipping RBF neural network adaptive control
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Adaptive output feedback control for nonlinear time-delay systems using neural network 被引量:9
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作者 Weisheng CHEN Junmin LI 《控制理论与应用(英文版)》 EI 2006年第4期313-320,共8页
This paper extends the adaptive neural network (NN) control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backsteppi... This paper extends the adaptive neural network (NN) control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay, Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on Lyapunov- Krasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved, The feasibility is investigated by two illustrative simulation examples. 展开更多
关键词 Time delay Nonlinear system neural network BACKSTEPPING Output feedback adaptive control
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Global approximation based adaptive RBF neural network control for supercavitating vehicles 被引量:11
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作者 LI Yang LIU Mingyong +1 位作者 ZHANG Xiaojian PENG Xingguang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第4期797-804,共8页
A global approximation based adaptive radial basis function(RBF) neural network control strategy is proposed for the trajectory tracking control of supercavitating vehicles(SV).A nominal model is built firstly wit... A global approximation based adaptive radial basis function(RBF) neural network control strategy is proposed for the trajectory tracking control of supercavitating vehicles(SV).A nominal model is built firstly with the unknown disturbance.Next, the control scheme is established consisting of a computed torque controller(CTC) for the practical vehicle and an RBF neural network controller to estimate model error between the practical vehicle and the nominal model. The network weights are adapted by employing a Lyapunov-based design. Then it is shown by the Lyapunov theory that the trajectory tracking errors asymptotically converge to a small neighborhood of zero. The control performance of the proposed controller is illustrated by simulation. 展开更多
关键词 radial basis function (RBF) neural network computedtorque controller (CTC) adaptive control supercavitating vehicle(SV)
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Adaptive H~∞ Control of Nonlinear Systems with Neural Networks 被引量:6
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作者 姜长生 陈谋 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2003年第1期36-41,共6页
The discussion is devoted to the adaptive H ∞ control method based on RBF neural networks for uncertain nonlinear systems in this paper. The controller consists of an equivalent controller and an H ∞ cont... The discussion is devoted to the adaptive H ∞ control method based on RBF neural networks for uncertain nonlinear systems in this paper. The controller consists of an equivalent controller and an H ∞ controller. The RBF neural networks are used to approximate the nonlinear functions and the approximation errors of the neural networks are used in the adaptive law to improve the performance of the systems. The H ∞ controller is designed for attenuating the influence of external disturbance and neural network approximation errors. The controller can not only guarantee stability of the nonlinear systems, but also attenuate the effect of the external disturbance and neural networks approximation errors to reach performance indexes. Finally, an example validates the effectiveness of this method. 展开更多
关键词 neural networks nonlinear systems adaptive control H control
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Adaptive Neural Network-Based Control for a Class of Nonlinear Pure-Feedback Systems With Time-Varying Full State Constraints 被引量:14
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作者 Tingting Gao Yan-Jun Liu +3 位作者 Senior Member IEEE Lei Liu Dapeng Li 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第5期923-933,共11页
Abstract--In this paper, an adaptive neural network (NN) control approach is proposed for nonlinear pure-feedback sys- tems with time-varying full state constraints. The pure-feedback systems of this paper are assum... Abstract--In this paper, an adaptive neural network (NN) control approach is proposed for nonlinear pure-feedback sys- tems with time-varying full state constraints. The pure-feedback systems of this paper are assumed to possess nonlinear function uncertainties. By using the mean value theorem, pure-feedback systems can be transformed into strict feedback forms. For the newly generated systems, NNs are employed to approximate unknown items. Based on the adaptive control scheme and backstepping algorithm, an intelligent controller is designed. At the same time, time-varying Barrier Lyapunov functions (BLFs) with error variables are adopted to avoid violating full state constraints in every step of the backstepping design. All closed- loop signals are uniformly ultimately bounded and the output tracking error converges to the neighborhood of zero, which can be verified by using the Lyapunov stability theorem. Two simulation examples reveal the performance of the adaptive NN control approach. Index TermsmAdaptive control, neural networks (NNs), non- linear pure-feedback systems, time-varying constraints. 展开更多
关键词 adaptive control neural networks(NNs) nonlinear pure-feedback systems time-varying constraints
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Adaptive RBF neural network control of robot with actuator nonlinearities 被引量:6
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作者 Jinkun LIU, Yu LU (School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China) 《控制理论与应用(英文版)》 EI 2010年第2期249-256,共8页
In this paper, an adaptive neural network control scheme for robot manipulators with actuator nonlinearities is presented. The control scheme consists of an adaptive neural network controller and an actuator nonlinear... In this paper, an adaptive neural network control scheme for robot manipulators with actuator nonlinearities is presented. The control scheme consists of an adaptive neural network controller and an actuator nonlinearities compensator. Since the actuator nonlinearities are usually included in the robot driving motor, a compensator using radial basis function (RBF) network is proposed to estimate the actuator nonlinearities and eliminate their effects. Subsequently, an adaptive neural network controller that neither requires the evaluation of inverse dynamical model nor the time-consuming training process is given. In addition, GL matrix and its product operator are introduced to help prove the stability of the closed control system. Considering the adaptive neural network controller and the RBF network compensator as the whole control scheme, the closed-loop system is proved to be uniformly ultimately bounded (UUB). The whole scheme provides a general procedure to control the robot manipulators with actuator nonlinearities. Simulation results verify the effectiveness of the designed scheme and the theoretical discussion. 展开更多
关键词 adaptive control RBF neural network Actuator nonlinearity Robot manipulator DEADZONE
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Adaptive Backstepping Terminal Sliding Mode Control Method Based on Recurrent Neural Networks for Autonomous Underwater Vehicle 被引量:12
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作者 Chao Yang Feng Yao Ming-Jun Zhang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2018年第6期228-243,共16页
The trajectory tracking control problem is addressed for autonomous underwater vehicle(AUV) in marine environ?ment, with presence of the influence of the uncertain factors including ocean current disturbance, dynamic ... The trajectory tracking control problem is addressed for autonomous underwater vehicle(AUV) in marine environ?ment, with presence of the influence of the uncertain factors including ocean current disturbance, dynamic modeling uncertainty, and thrust model errors. To improve the trajectory tracking accuracy of AUV, an adaptive backstepping terminal sliding mode control based on recurrent neural networks(RNN) is proposed. Firstly, considering the inaccu?rate of thrust model of thruster, a Taylor’s polynomial is used to obtain the thrust model errors. And then, the dynamic modeling uncertainty and thrust model errors are combined into the system model uncertainty(SMU) of AUV; through the RNN, the SMU and ocean current disturbance are classified, approximated online. Finally, the weights of RNN and other control parameters are adjusted online based on the backstepping terminal sliding mode controller. In addition, a chattering?reduction method is proposed based on sigmoid function. In chattering?reduction method, the sigmoid function is used to realize the continuity of the sliding mode switching function, and the sliding mode switching gain is adjusted online based on the exponential form of the sliding mode function. Based on the Lyapu?nov theory and Barbalat’s lemma, it is theoretically proved that the AUV trajectory tracking error can quickly converge to zero in the finite time. This research proposes a trajectory tracking control method of AUV, which can e ectively achieve high?precision trajectory tracking control of AUV under the influence of the uncertain factors. The feasibility and e ectiveness of the proposed method is demonstrated with trajectory tracking simulations and pool?experi?ments of AUV. 展开更多
关键词 Autonomous underwater vehicle(AUV) Trajectory tracking neural networks Backstepping method Terminal sliding mode adaptive control
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Adaptive neural network tracking control for a class of unknown nonlinear time-delay systems 被引量:5
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作者 Chen Weisheng Li Junmin 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第3期611-618,共8页
For a class of unknown nonlinear time-delay systems, an adaptive neural network (NN) control design approach is proposed. Backstepping, domination and adaptive bounding design technique are combined to construct a r... For a class of unknown nonlinear time-delay systems, an adaptive neural network (NN) control design approach is proposed. Backstepping, domination and adaptive bounding design technique are combined to construct a robust memoryless adaptive NN tracking controller. Unknown time-delay functions are approximated by NNs, such that the requirement on the nonlinear time-delay functions is relaxed. Based on Lyapunov-Krasoviskii functional, the sem-global uniformly ultimately boundedness (UUB) of all the signals in the closed-loop system is proved. The arbitrary output tracking accuracy is achieved by tuning the design parameters. The feasibility is investigated by an illustrative simulation example. 展开更多
关键词 nonlinear time-delay system neural network adaptive bounding technique memoryless adaptive NN controller.
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Neural network based adaptive sliding mode control of uncertain nonlinear systems 被引量:4
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作者 Ghania Debbache Noureddine Goléa 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第1期119-128,共10页
The purpose of this paper is the design of neural network-based adaptive sliding mode controller for uncertain unknown nonlinear systems. A special architecture adaptive neural network, with hyperbolic tangent activat... The purpose of this paper is the design of neural network-based adaptive sliding mode controller for uncertain unknown nonlinear systems. A special architecture adaptive neural network, with hyperbolic tangent activation functions, is used to emulate the equivalent and switching control terms of the classic sliding mode control (SMC). Lyapunov stability theory is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as of all other signals in the closed loop. In addition to keeping the stability and robustness properties of the SMC, the neural network-based adaptive sliding mode controller exhibits perfect rejection of faults arising during the system operating. Simulation studies are used to illustrate and clarify the theoretical results. 展开更多
关键词 nonlinear system neural network sliding mode con- trol (SMC) adaptive control stability robustness.
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Adaptive control of system with hysteresis using neural networks 被引量:4
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作者 Li Chuntao Tan Yonghong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第1期163-167,共5页
An adaptive control scheme is developed for a class of single-input nonlinear systems preceded by unknown hysteresis, which is a non-differentiable and multi-value mapping nonlinearity. The controller based on the thr... An adaptive control scheme is developed for a class of single-input nonlinear systems preceded by unknown hysteresis, which is a non-differentiable and multi-value mapping nonlinearity. The controller based on the three-layer neural network (NN), whose weights are derived from Lyapunov stability analysis, guarantees closed-loop semiglobal stability and convergence of the tracking errors to a small residual set. An example is used to confirm the effectiveness of the proposed control scheme. 展开更多
关键词 neural networks HYSTERESIS adaptive control preisach model.
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Neural Network Based Adaptive Tracking Control for a Class of Pure Feedback Nonlinear Systems With Input Saturation 被引量:7
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作者 Nassira Zerari Mohamed Chemachema Najib Essounbouli 《IEEE/CAA Journal of Automatica Sinica》 EI CSCD 2019年第1期278-290,共13页
In this paper, an adaptive neural networks(NNs)tracking controller is proposed for a class of single-input/singleoutput(SISO) non-affine pure-feedback non-linear systems with input saturation. In the proposed approach... In this paper, an adaptive neural networks(NNs)tracking controller is proposed for a class of single-input/singleoutput(SISO) non-affine pure-feedback non-linear systems with input saturation. In the proposed approach, the original input saturated nonlinear system is augmented by a low pass filter.Then, new system states are introduced to implement states transformation of the augmented model. The resulting new model in affine Brunovsky form permits direct and simpler controller design by avoiding back-stepping technique and its complexity growing as done in existing methods in the literature.In controller design of the proposed approach, a state observer,based on the strictly positive real(SPR) theory, is introduced and designed to estimate the new system states, and only two neural networks are used to approximate the uncertain nonlinearities and compensate for the saturation nonlinearity of actuator. The proposed approach can not only provide a simple and effective way for construction of the controller in adaptive neural networks control of non-affine systems with input saturation, but also guarantee the tracking performance and the boundedness of all the signals in the closed-loop system. The stability of the control system is investigated by using the Lyapunov theory. Simulation examples are presented to show the effectiveness of the proposed controller. 展开更多
关键词 adaptive control INPUT SATURATION neural networks systems (NNs) nonlinear pure-feedback
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Adaptive Neural Network Dynamic Surface Control for Perturbed Nonlinear Time-delay Systems 被引量:4
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作者 Geng Ji 《International Journal of Automation and computing》 EI 2012年第2期135-141,共7页
This paper proposes an adaptive neural network control method for a class of perturbed strict-feedback nonlinear systems with unknown time delays. Radial basis function neural networks are used to approximate unknown ... This paper proposes an adaptive neural network control method for a class of perturbed strict-feedback nonlinear systems with unknown time delays. Radial basis function neural networks are used to approximate unknown intermediate control signals. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown time delay terms have been compensated. Dynamic surface control technique is used to overcome the problem of "explosion of complexity" in backstepping design procedure. In addition, the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system is proved. A main advantage of the proposed controller is that both problems of "curse of dimensionality" and "explosion of complexity" are avoided simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the approach. 展开更多
关键词 adaptive control dynamic surface control neural network nonlinear time delay system stability analysis.
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Adaptive control of parallel manipulators via fuzzy-neural network algorithm 被引量:3
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作者 Dachang ZHU Yuefa FANG 《控制理论与应用(英文版)》 EI 2007年第3期295-300,共6页
This paper considers adaptive control of parallel manipulators combined with fuzzy-neural network algorithms (FNNA). With this algorithm, the robustness is guaranteed by the adaptive control law and the parametric u... This paper considers adaptive control of parallel manipulators combined with fuzzy-neural network algorithms (FNNA). With this algorithm, the robustness is guaranteed by the adaptive control law and the parametric uncertainties are eliminated. FNNA is used to handle model uncertainties and external disturbances. In the proposed control scheme, we consider modifying the weight of fuzzy rules and present these rules to a MIMO system of parallel manipulators with more than three degrees-of-freedom (DoF). The algorithm has the advantage of not requiring the inverse of the Jacobian matrix especially for the low DoF parallel manipulators. The validity of the control scheme is shown through numerical simulations of a 6-RPS parallel manipulator with three DoF. 展开更多
关键词 Parallel manipulator adaptive control Fuzzy neural network algorithm SIMULATION
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Adaptive Neural Network Control with Control Allocation for A Manned Submersible in Deep Sea 被引量:2
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作者 俞建成 张艾群 +1 位作者 王晓辉 吴宝举 《China Ocean Engineering》 SCIE EI 2007年第1期147-161,共15页
This paper thoroughly studies a control system with control allocation for a manned submersible in deep sea being developed in China. The proposed control system consists of a neural-network-based direct adaptive cont... This paper thoroughly studies a control system with control allocation for a manned submersible in deep sea being developed in China. The proposed control system consists of a neural-network-based direct adaptive controller and a dynamic control allocation module. A control energy cost function is used as the optimization criteria of the control allocation module, and weighted pseudo-inverse is used to find the solution of the control allocation problem. In the presence of bounded unknown disturbance and neural networks approximation error, stability of the closed-loop control system of manned submersible is proved with Lyaponov theory. The feasibility and validity of the proposed control system is further verified through experiments conducted on a semi-physical simulation platform for the manned submersible in deep sea. 展开更多
关键词 manned submersibles neural networks adaptive control control allocation underwater vehicles
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Neural-network adaptive controller for nonlinear systems and its application in pneumatic servo systems 被引量:2
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作者 Lu LU Fagui LIU Weixiang SHI 《控制理论与应用(英文版)》 EI 2008年第1期97-103,共7页
In this paper, a novel control law is presented, which uses neural-network techniques to approximate the affine class nonlinear system having unknown or uncertain dynamics and noise disturbances. It adopts an adaptive... In this paper, a novel control law is presented, which uses neural-network techniques to approximate the affine class nonlinear system having unknown or uncertain dynamics and noise disturbances. It adopts an adaptive control law to adjust the network parameters online and adds another control component according to H-infinity control theory to attenuate the disturbance. This control law is applied to the position tracking control of pneumatic servo systems. Simulation and experimental results show that the tracking precision and convergence speed is obviously superior to the results by using the basic BP-network controller and self-tuning adaptive controller. 展开更多
关键词 Nonlinear control CONVERGENCE adaptive control H-infinity control neural networks Pneumatic servo system
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Decentralized direct adaptive neural network control for a class of interconnected systems 被引量:2
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作者 Zhang Tianping Mei Jiandong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第2期374-380,共7页
The problem of direct adaptive neural network control for a class of large-scale systems with unknown function control gains and the high-order interconneetions is studied in this paper. Based on the principle of slid... The problem of direct adaptive neural network control for a class of large-scale systems with unknown function control gains and the high-order interconneetions is studied in this paper. Based on the principle of sliding mode control and the approximation capability of multilayer neural networks, a design scheme of decentralized di- rect adaptive sliding mode controller is proposed. The plant dynamic uncertainty and modeling errors are adaptively compensated by adjusted the weights and sliding mode gains on-line for each subsystem using only local informa- tion. According to the Lyapunov method, the closed-loop adaptive control system is proven to be globally stable, with tracking errors converging to a neighborhood of zero. Simulation results demonstrate the effectiveness of the proposed approach. 展开更多
关键词 neural networks decentralized control sliding mode control adaptive control global stability.
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