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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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Time-varying parameters estimation with adaptive neural network EKF for missile-dual control system
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作者 YUAN Yuqi ZHOU Di +1 位作者 LI Junlong LOU Chaofei 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2024年第2期451-462,共12页
In this paper, a filtering method is presented to estimate time-varying parameters of a missile dual control system with tail fins and reaction jets as control variables. In this method, the long-short-term memory(LST... In this paper, a filtering method is presented to estimate time-varying parameters of a missile dual control system with tail fins and reaction jets as control variables. In this method, the long-short-term memory(LSTM) neural network is nested into the extended Kalman filter(EKF) to modify the Kalman gain such that the filtering performance is improved in the presence of large model uncertainties. To avoid the unstable network output caused by the abrupt changes of system states,an adaptive correction factor is introduced to correct the network output online. In the process of training the network, a multi-gradient descent learning mode is proposed to better fit the internal state of the system, and a rolling training is used to implement an online prediction logic. Based on the Lyapunov second method, we discuss the stability of the system, the result shows that when the training error of neural network is sufficiently small, the system is asymptotically stable. With its application to the estimation of time-varying parameters of a missile dual control system, the LSTM-EKF shows better filtering performance than the EKF and adaptive EKF(AEKF) when there exist large uncertainties in the system model. 展开更多
关键词 long-short-term memory(LSTM)neural network extended Kalman filter(EKF) rolling training time-varying parameters estimation missile dual control system
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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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Intelligent Flow Control Technique of ABR Service in ATM Networks Based on Fuzzy Neural Networks 被引量:7
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作者 Zhang Liangjie Li Yanda Li Qinghua Wang Pu (Dept of Automation, Tsinghua University, Beijing 100084) 《通信学报》 EI CSCD 北大核心 1997年第3期3-9,共7页
InteligentFlowControlTechniqueofABRServiceinATMNetworksBasedonFuzzyNeuralNetworks①ZhangLiangjieLiYandaLiQing... InteligentFlowControlTechniqueofABRServiceinATMNetworksBasedonFuzzyNeuralNetworks①ZhangLiangjieLiYandaLiQinghuaWangPu(DeptofA... 展开更多
关键词 模糊神经网络 流量控制 异步传输网 反馈 可用位率
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Fuzzy Control Based on Neural Networks for Armored Vehicle Electric Drive System 被引量:1
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作者 马晓军 李华 +1 位作者 张剑 张豫南 《Defence Technology(防务技术)》 SCIE EI CAS 2006年第3期169-172,共4页
关键词 装甲车 电力驱动 模糊控制 神经网络 鲁棒性
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Study on the Robot Robust Adaptive Control Based on Neural Networks
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作者 温淑焕 王洪瑞 吴丽艳 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2003年第4期55-58,共4页
Force control based on neural networks is presented. Under the framework of hybrid control, an RBF neural network is used to compensate for all the uncertainties from robot dynamics and unknown environment first. The ... Force control based on neural networks is presented. Under the framework of hybrid control, an RBF neural network is used to compensate for all the uncertainties from robot dynamics and unknown environment first. The technique will improve the adaptability to environment stiffness when the end-effector is in contact with the environment, and does not require any a priori knowledge on the upper bound of syste uncertainties. Moreover, it need not compute the inverse of inertia matrix. Learning algorithms for neural networks to minimize the force error directly are designed. Simulation results have shown a better force/position tracking when neural network is used. 展开更多
关键词 ROBOTICS force/position control neural network hybrid control.
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An intelligent control method based on artificial neural network for numerical flight simulation of the basic finner projectile with pitching maneuver 被引量:1
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作者 Yiming Liang Guangning Li +3 位作者 Min Xu Junmin Zhao Feng Hao Hongbo Shi 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2024年第2期663-674,共12页
In this paper,an intelligent control method applying on numerical virtual flight is proposed.The proposed algorithm is verified and evaluated by combining with the case of the basic finner projectile model and shows a... In this paper,an intelligent control method applying on numerical virtual flight is proposed.The proposed algorithm is verified and evaluated by combining with the case of the basic finner projectile model and shows a good application prospect.Firstly,a numerical virtual flight simulation model based on overlapping dynamic mesh technology is constructed.In order to verify the accuracy of the dynamic grid technology and the calculation of unsteady flow,a numerical simulation of the basic finner projectile without control is carried out.The simulation results are in good agreement with the experiment data which shows that the algorithm used in this paper can also be used in the design and evaluation of the intelligent controller in the numerical virtual flight simulation.Secondly,combined with the real-time control requirements of aerodynamic,attitude and displacement parameters of the projectile during the flight process,the numerical simulations of the basic finner projectile’s pitch channel are carried out under the traditional PID(Proportional-Integral-Derivative)control strategy and the intelligent PID control strategy respectively.The intelligent PID controller based on BP(Back Propagation)neural network can realize online learning and self-optimization of control parameters according to the acquired real-time flight parameters.Compared with the traditional PID controller,the concerned control variable overshoot,rise time,transition time and steady state error and other performance indicators have been greatly improved,and the higher the learning efficiency or the inertia coefficient,the faster the system,the larger the overshoot,and the smaller the stability error.The intelligent control method applying on numerical virtual flight is capable of solving the complicated unsteady motion and flow with the intelligent PID control strategy and has a strong promotion to engineering application. 展开更多
关键词 Numerical virtual flight Intelligent control BP neural network PID Moving chimera grid
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Rapid optimal control law generation: an MoE based method
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作者 ZHANG Tengfei SU Hua +2 位作者 GONG Chunlin YANG Sizhi BAI Shaobo 《Journal of Systems Engineering and Electronics》 2025年第1期280-291,共12页
To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target... To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target location. Since trajectory optimization struggles to meet real-time requirements, the emergence of data-based generation methods has become a significant focus in contemporary research. However, due to the large differences in the characteristics of the optimal control laws caused by the diversity of tasks, it is difficult to achieve good prediction results by modeling all data with one single model.Therefore, the modeling idea of the mixture of experts(MoE) is adopted. Firstly, the K-means clustering algorithm is used to partition the sample data set, and the corresponding neural network classification model is established as the gate switch of MoE. Then, the expert models, i.e., the mappings from the generation conditions to the optimal control law represented by the results of principal component analysis(PCA), are represented by Kriging models. Finally, multiple rounds of accuracy evaluation, sample supplementation, and model updating are conducted to improve the generation accuracy. The Monte Carlo simulation shows that the accuracy of the proposed model reaches 96% and the generation efficiency meets the real-time requirement. 展开更多
关键词 optimal control mixture of experts(MoE) K-MEANS Kriging model neural network classification principal component analysis(PCA)
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Adaptive Fuzzy Control for a Class of MIMO Nonlinear Systems with Unknown Dead-zones 被引量:14
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作者 ZHANG Tian-Ping YI Yang 《自动化学报》 EI CSCD 北大核心 2007年第1期96-100,共5页
A design scheme of adaptive fuzzy controller for a class of uncertain MIMO nonlinear systems with unknown dead-zones and a triangular control structure is proposed in this pa-per.The design is based on the principle o... A design scheme of adaptive fuzzy controller for a class of uncertain MIMO nonlinear systems with unknown dead-zones and a triangular control structure is proposed in this pa-per.The design is based on the principle of sliding mode control and the property of Nussbaum function.The approach does not require a priori knowledge of the signs of the control gains and the upper bounds and lower bounds of dead-zone parameters to be known a priori.By introducing the integral-type Lyapunov function and adopting the adaptive compensation term of the upper bound of the optimal approximation error and the dead-zone disturbance,the closed-loop control system is proved to be semi-globally stable in the sense that all signals involved are bounded,with tracking errors converging to zero. 展开更多
关键词 DEAD-ZONE fuzzy control adaptive control sliding mode control Nussbaum function
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Global approximation based adaptive RBF neural network control for supercavitating vehicles 被引量:12
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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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Backstepping sliding mode control for uncertain strict-feedback nonlinear systems using neural-network-based adaptive gain scheduling 被引量:14
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作者 YANG Yueneng YAN Ye 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第3期580-586,共7页
A neural-network-based adaptive gain scheduling backstepping sliding mode control(NNAGS-BSMC) approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain st... A neural-network-based adaptive gain scheduling backstepping sliding mode control(NNAGS-BSMC) approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain strict-feedback nonlinear systems is formulated. Second, the detailed design of NNAGSBSMC is described. The sliding mode control(SMC) law is designed to track a referenced output via backstepping technique.To decrease chattering result from SMC, a radial basis function neural network(RBFNN) is employed to construct the NNAGSBSMC to facilitate adaptive gain scheduling, in which the gains are scheduled adaptively via neural network(NN), with sliding surface and its differential as NN inputs and the gains as NN outputs. Finally, the verification example is given to show the effectiveness and robustness of the proposed approach. Contrasting simulation results indicate that the NNAGS-BSMC decreases the chattering effectively and has better control performance against the BSMC. 展开更多
关键词 backstepping control sliding mode control(SMC) neural network(NN) strict-feedback system chattering decrease
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Adaptive fuzzy sliding mode control for robotic airship with model uncertainty and external disturbance 被引量:6
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作者 Yueneng Yang Jie Wu Wei Zheng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第2期250-255,共6页
An adaptive fuzzy sliding mode control (AFSMC) ap- proach is proposed for a robotic airship. First, the mathematical model of an airship is derived in the form of a nonlinear control system. Second, an AFSMC approac... An adaptive fuzzy sliding mode control (AFSMC) ap- proach is proposed for a robotic airship. First, the mathematical model of an airship is derived in the form of a nonlinear control system. Second, an AFSMC approach is proposed to design the attitude control system of airship, and the global stability of the closed-loop system is proved by using the Lyapunov stability theorem. Finally, simulation results verify the effectiveness and robustness of the proposed control approach in the presence of model uncertainties and external disturbances. 展开更多
关键词 flight control sliding mode fuzzy system adaptation law station keeping airship.
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Adaptive Fuzzy Control System of Servomechanism for Electro-Discharge Machining Combined with Ultrasonic Vibration 被引量:6
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作者 ZHANG Jian-hua, ZHANG Hui, SU Da-shi, QIN Yong, HUO Meng-You, ZHANG Qin-he (College of Mechanical Engineering, Shandong University, Jinan 250061, China) 《厦门大学学报(自然科学版)》 CAS CSCD 北大核心 2002年第S1期64-65,共2页
For electro-discharge machining, only in the optimum state could the highest material removal rate be realized. In practical machining process, the timely elevation of the tool electrode is needed to eliminate chippin... For electro-discharge machining, only in the optimum state could the highest material removal rate be realized. In practical machining process, the timely elevation of the tool electrode is needed to eliminate chipping, which ordinarily occupies quite a lot of time. Therefore, besides the control of the machining parameters, the control of the optimum discharge gap and the conversion of different machining states is also needed. In this paper, the adaptive fuzzy control system of servomechanism for EDM combined with ultrasonic vibration is studied, the servomechanism of which is composed of the stepping motor comprising variable steps and the inductive synchronizer. The fuzzy control technology is used to realize the control of the frequency and the step of the servomechanism. The adaptive fuzzy controller has three inputs and two outputs, which can well meet the actual control requirements. The constitution of the fuzzy control regulation for the step frequency is the key to the design of the whole fuzzy control system of the servomechanism. The step frequency is mainly determined by the position error and the change rate of the position error. When the value of the position error is high or medium, the controlled parameters are selected to eliminate the error; when the position error is lower, the controlled parameters are selected to avoid the over-orientation and thus keep the stability of the system. According to these, a fuzzy control table is established in advanced, which is used to express the relations between the fuzzy input parameters and the fuzzy output parameters. The input parameters and the output parameters are all expressed by the level-values in fuzzy field. Therefore, the output parameters used for control can be obtained for the fuzzy control table according to the detected actual input parameters, by which the EDM combined with ultrasonic vibration is improved and the machining efficiency is increased. In addition, a stimulation program is designed by means of Microsoft Visual Basic 展开更多
关键词 combined machining SERVOMECHANISM adaptive fuzzy control system
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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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Application of neural networks for permanent magnet synchronous motor direct torque control 被引量:6
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作者 Zhang Chunmei Liu Heping +1 位作者 Chen Shujin Wang Fangjun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第3期555-561,共7页
Neural networks require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training a... Neural networks require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training algorithms. The application of neural networks to control interior permanent magnet synchronous motor using direct torque control (DTC) is discussed. A neural network is used to emulate the state selector of the DTC. The neural networks used are the back-propagation and radial basis function. To reduce the training patterns and increase the execution speed of the training process, the inputs of switching table are converted to digital signals, i.e., one bit represent the flux error, one bit the torque error, and three bits the region of stator flux. Computer simulations of the motor and neural-network system using the two approaches are presented and compared. Discussions about the back-propagation and radial basis function as the most promising training techniques are presented, giving its advantages and disadvantages. The system using back-propagation and radial basis function networks controller has quick parallel speed and high torque response. 展开更多
关键词 interior permanent magnet synchronous motor radial basis function neural network torque control direct torque control.
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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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Integrated guidance and control of guided projectile with multiple constraints based on fuzzy adaptive and dynamic surface 被引量:8
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作者 Shang Jiang Fu-qing Tian +1 位作者 Shi-yan Sun Wei-ge Liang 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2020年第6期1130-1141,共12页
Based on fuzzy adaptive and dynamic surface(FADS),an integrated guidance and control(IGC)approach was proposed for large caliber naval gun guided projectile,which was robust to target maneuver,canard dynamic character... Based on fuzzy adaptive and dynamic surface(FADS),an integrated guidance and control(IGC)approach was proposed for large caliber naval gun guided projectile,which was robust to target maneuver,canard dynamic characteristics,and multiple constraints,such as impact angle,limited measurement of line of sight(LOS)angle rate and nonlinear saturation of canard deflection.Initially,a strict feedback cascade model of IGC in longitudinal plane was established,and extended state observer(ESO)was designed to estimate LOS angle rate and uncertain disturbances with unknown boundary inside and outside of system,including aerodynamic parameters perturbation,target maneuver and model errors.Secondly,aiming at zeroing LOS angle tracking error and LOS angle rate in finite time,a nonsingular terminal sliding mode(NTSM)was designed with adaptive exponential reaching law.Furthermore,combining with dynamic surface,which prevented the complex differential of virtual control laws,the fuzzy adaptive systems were designed to approximate observation errors of uncertain disturbances and to reduce chatter of control law.Finally,the adaptive Nussbaum gain function was introduced to compensate nonlinear saturation of canard deflection.The LOS angle tracking error and LOS angle rate were convergent in finite time and whole system states were uniform ultimately bounded,rigorously proven by Lyapunov stability theory.Hardware-in-the-loop simulation(HILS)and digital simulation experiments both showed FADS provided guided projectile with good guidance performance while striking targets with different maneuvering forms. 展开更多
关键词 Integrated guidance and control Multiple constraints fuzzy adaptive Dynamic surface Nonsingular terminal sliding mode Extended state observer
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Adaptive control using interval Type-2 fuzzy logic for uncertain nonlinear systems 被引量:5
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作者 周海波 应浩 段吉安 《Journal of Central South University》 SCIE EI CAS 2011年第3期760-766,共7页
A new adaptive Type-2 (T2) fuzzy controller was developed and its potential performance advantage over adaptive Type-1 (T1) fuzzy control was also quantified in computer simulation. Base on the Lyapunov method, th... A new adaptive Type-2 (T2) fuzzy controller was developed and its potential performance advantage over adaptive Type-1 (T1) fuzzy control was also quantified in computer simulation. Base on the Lyapunov method, the adaptive laws with guaranteed system stability and convergence were developed. The controller updates its parameters online using the laws to control a system and tracks its output command trajectory. The simulation study involving the popular inverted pendulum control problem shows theoretically predicted system stability and good tracking performance. And the comparison simulation experiments subjected to white noige or step disturbance indicate that the T2 controller is better than the T1 controller by 0--18%, depending on the experiment condition and performance measure. 展开更多
关键词 Type-2 fuzzy systems adaptive fuzzy control nonlinear systems stability
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Research of robust adaptive trajectory linearization control based on T-S fuzzy system 被引量:3
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作者 Jiang Changsheng Zhang Chunyu Zhu Liang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第3期537-545,共9页
A robust adaptive trajectory linearization control (RATLC) algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertai... A robust adaptive trajectory linearization control (RATLC) algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertainty are estimated by the T-S fuzzy system, and a robust adaptive control law is designed by the Lyapunov theory. Irrespective of whether the dimensions of the system and the rules of the fuzzy system are large or small, there is only one parameter adjusting on line. Uniformly ultimately boundedness of all signals of the composite closed-loop system are proved by theory analysis. Finally, a numerical example is studied based on the proposed method. The simulation results demonstrate the effectiveness and robustness of the control scheme. 展开更多
关键词 nonlinear system trajectory linearization control robust adaptive control T-S fuzzy system.
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Adaptive neural network based sliding mode altitude control for a quadrotor UAV 被引量:4
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作者 Hadi RAZMI 《Journal of Central South University》 SCIE EI CAS CSCD 2018年第11期2654-2663,共10页
Reasons and realities such as being non-linear of dynamical equations,being lightweight and unstable nature of quadrotor,along with internal and external disturbances and parametric uncertainties,have caused that the ... Reasons and realities such as being non-linear of dynamical equations,being lightweight and unstable nature of quadrotor,along with internal and external disturbances and parametric uncertainties,have caused that the controller design for these quadrotors is considered the challenging issue of the day.In this work,an adaptive sliding mode controller based on neural network is proposed to control the altitude of a quadrotor.The error and error derivative of the altitude of a quadrotor are the inputs of neural network and altitude sliding surface variable is its output.Neural network estimates the sliding surface variable adaptively according to the conditions of quadrotor and sets the altitude of a quadrotor equal to the desired value.The proposed controller stability has been proven by Lyapunov theory and it is shown that all system states reach to sliding surface and are remaining in it.The superiority of the proposed control method has been proven by comparison and simulation results. 展开更多
关键词 adaptive sliding mode controller analog neural network(ANN) altitude control of quadrotor parametric uncertainty
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