The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematica...The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established.展开更多
The control of gas fractionation unit(GFU) in petroleum industry is very difficult due to multivariable characteristics and a large time delay.PID controllers are still applied in most industry processes.However,the t...The control of gas fractionation unit(GFU) in petroleum industry is very difficult due to multivariable characteristics and a large time delay.PID controllers are still applied in most industry processes.However,the traditional PID control has been proven not sufficient and capable for this particular petro-chemical process.In this work,an incremental multivariable predictive functional control(IMPFC) algorithm was proposed with less online computation,great precision and fast response.An incremental transfer function matrix model was set up through the step-response data,and predictive outputs were deduced with the theory of single-value optimization.The results show that the method can optimize the incremental control variable and reject the constraint of the incremental control variable with the positional predictive functional control algorithm,and thereby making the control variable smoother.The predictive output error and future set-point were approximated by a polynomial,which can overcome the problem under the model mismatch and make the predictive outputs track the reference trajectory.Then,the design of incremental multivariable predictive functional control was studied.Simulation and application results show that the proposed control strategy is effective and feasible to improve control performance and robustness of process.展开更多
The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapuno...The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method.展开更多
Reaction control system(RCS) is a powerful and efficient actuator for space vehicles attitude control, which is typically characterized as a pulsed unilateral effector only with two states(off/on). Along with inevitab...Reaction control system(RCS) is a powerful and efficient actuator for space vehicles attitude control, which is typically characterized as a pulsed unilateral effector only with two states(off/on). Along with inevitable internal uncertainties and external disturbances in practice, this inherent nonlinear character always hinders space vehicles autopilot from pursuing precise tracking performance. Compared to most of pre-existing methodologies that passively suppress the uncertainties and disturbances, a design based on predictive functional control(PFC) and generalized extended state observer(GESO) is firstly proposed for three-axis RCS control system to actively reject that with no requirement for additional fuel consumption. To obtain a high fidelity predictive model on which the performance of PFC greatly depends, the nonlinear coupling multiple-input multiple-output(MIMO) flight dynamics model is parameterized as a state-dependent coefficient form. And based on that, a MIMO PFC algorithm in state space domain for a plant of arbitrary orders is deduced in this paper.The internal uncertainties and external disturbances are lumped as a total disturbance, which is estimated and cancelled timely to further enhance the robustness. The continuous control command synthesised by above controller-rejector tandem is finally modulated by pulse width pulse frequency modulator(PWPF) to on-off signals to meet RCS requirement. The robustness and feasibility of the proposed design are validated by a series of performance comparison simulations with some prominent methods in the presence of significant perturbations and disturbances, as well as measurement noise.展开更多
A method is developed by which control Lyapunov functions of a class of nonlinear systems can be constructed systematically. Based on the control Lyapunov function, a feedback control is obtained to stabilize the clos...A method is developed by which control Lyapunov functions of a class of nonlinear systems can be constructed systematically. Based on the control Lyapunov function, a feedback control is obtained to stabilize the closed-loop system. In addition, this method is applied to stabilize the Benchmark system. A simulation shows the effectiveness of the method.展开更多
The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this cond...The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.展开更多
In order to obtain accurate prediction model and compensate for the influence of model mismatch on the control performance of the system and avoid solving nonlinear programming problem,an adaptive fuzzy predictive fun...In order to obtain accurate prediction model and compensate for the influence of model mismatch on the control performance of the system and avoid solving nonlinear programming problem,an adaptive fuzzy predictive functional control(AFPFC) scheme for multivariable nonlinear systems was proposed.Firstly,multivariable nonlinear systems were described based on Takagi-Sugeno(T-S) fuzzy models;assuming that the antecedent parameters of T-S models were kept,the consequent parameters were identified on-line by using the weighted recursive least square(WRLS) method.Secondly,the identified T-S models were linearized to be time-varying state space model at each sampling instant.Finally,by using linear predictive control technique the analysis solution of the optimal control law of AFPFC was established.The application results for pH neutralization process show that the absolute error between the identified T-S model output and the process output is smaller than 0.015;the tracking ability of the proposed AFPFC is superior to that of non-AFPFC(NAFPFC) for pH process without disturbances,the overshoot of the effluent pH value of AFPFC with disturbances is decreased by 50% compared with that of NAFPFC;when the process parameters of AFPFC vary with time the integrated absolute error(IAE) performance index still retains to be less than 200 compared with that of NAFPFC.展开更多
The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature. First, the so-called stochastic LaSalle theory is...The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature. First, the so-called stochastic LaSalle theory is extended to some extent, and accordingly, the results of global ultimate boundedness for stochastic nonlinear systems are developed. Next, a new design scheme of fuzzy adaptive control is proposed. The advantage of it is that it does not require priori knowledge of virtual control gain function sign, which is usually demanded in many designs. At the same time, the track performance of closed-loop systems is improved by adaptive modifying the estimated error upper bound. By theoretical analysis, the signals of closed-loop systems are globally ultimately bounded in probability and the track error converges to a small residual set around the origin in 4th-power expectation.展开更多
A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimiza...A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.展开更多
In this paper, adaptive identification and control of nonlinear dynamical systems are investigated using radial basis function networks (RBF). Firstly, a novel approach to train the RBF is introduced, which employs an...In this paper, adaptive identification and control of nonlinear dynamical systems are investigated using radial basis function networks (RBF). Firstly, a novel approach to train the RBF is introduced, which employs an adaptive fuzzy generalized learning vector quantization (AFGLVQ) technique and recursive least squares algorithm with variable forgetting factor (VRLS). The AFGLVQ adjusts the centers of the RBF while the VRLS updates the connection weights of the network. The identification algorithm has the properties of rapid convergence and persistent adaptability that make it suitable for real-time control. Secondly, on the basis of the one-step ahead RBF predictor, the control law is optimized iteratively through a numerical stable Davidon's least squares-based (SDLS) minimization approach. Four nonlinear examples are simulated to demonstrate the effectiveness of the identification and control algorithms.展开更多
The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding L...The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding Legendre series. Matching the first three terms of the Legendre series of the loop gain with the desired one gives the PID controller parameters. The closed loop system stability conditions in terms of the Legendre basis function pole(λ) for a wide range of systems including the first order, second order, double integrator, first order plus dead time, and first order unstable plants are obtained. For first order and double integrator plants, the closed loop system stability is preserved for all values of λ and for the other plants, an appropriate range in terms of λ is obtained. The optimum value of λ to attain a minimum integral square error performance index in the presence of the control signal constraints is achieved. The numerical simulations demonstrate the benefits of the Legendre based PID controller.展开更多
An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network （FTRBFNN） is presented for a general class of strict-feedback nonlinear systems,which may possess a wid...An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network （FTRBFNN） is presented for a general class of strict-feedback nonlinear systems,which may possess a wide class of uncertainties that are not linearly parameterized and do not have any prior knowledge of the bounding functions.FTRBFNN is employed to approximate the uncertainty online,and a systematic framework for adaptive controller design is given by dynamic surface control. The control algorithm has two outstanding features,namely,the neural network regulates the weights,width and center of Gaussian function simultaneously,which ensures the control system has perfect ability of restraining different unknown uncertainties and the integral term of tracking error introduced in the control law can eliminate the static error of the closed loop system effectively. As a result,high control precision can be achieved.All signals in the closed loop system can be guaranteed bounded by Lyapunov approach.Finally,simulation results demonstrate the validity of the control approach.展开更多
The control law design for a near-space hypersonic vehicle（NHV） is highly challenging due to its inherent nonlinearity,plant uncertainties and sensitivity to disturbances.This paper presents a novel functional link ...The control law design for a near-space hypersonic vehicle（NHV） is highly challenging due to its inherent nonlinearity,plant uncertainties and sensitivity to disturbances.This paper presents a novel functional link network（FLN） control method for an NHV with dynamical thrust and parameter uncertainties.The approach devises a new partially-feedback-functional-link-network（PFFLN） adaptive law and combines it with the nonlinear generalized predictive control（NGPC） algorithm.The PFFLN is employed for approximating uncertainties in flight.Its weights are online tuned based on Lyapunov stability theorem for the first time.The learning process does not need any offline training phase.Additionally,a robust controller with an adaptive gain is designed to offset the approximation error.Finally,simulation results show a satisfactory performance for the NHV attitude tracking,and also illustrate the controller＇s robustness.展开更多
大豆分离蛋白(Soy Protein Isolate,SPI)功能特性决定应用领域,加工过程中NaOH添加量影响SPI功能特性。文章究利用Matlab模拟,采用传统比例积分微分(proportional integral derivative,PID)和模糊自适应控制(Adaptive Fuzzy Control,AFC...大豆分离蛋白(Soy Protein Isolate,SPI)功能特性决定应用领域,加工过程中NaOH添加量影响SPI功能特性。文章究利用Matlab模拟,采用传统比例积分微分(proportional integral derivative,PID)和模糊自适应控制(Adaptive Fuzzy Control,AFC)方法调控NaOH,中和大豆凝乳,并分析其对SPI结构和功能特性的影响。结果表明,pH值为7时,常规PID控制方法NaOH超调量为1.86%,调节时间为47.1 s;模糊自适应控制方法无超调量,调节时间为35.8 s。模糊自适应控制下,SPI傅里叶红外光谱吸收峰更稳定,紫外吸收特性更佳,二级结构向有序转变,表面疏水性较高,且溶解性、起泡性、泡沫稳定性、乳化性和乳化稳定性均优于常规PID控制方法。展开更多
基金Supported by Natural Science Foundation of Zhejiang Province P. R. China (Y105141)Natural Science Foundation of Fujian Province P.R.China (A0510025)Technological Project of Zhejiang Education Department,P. R. China(20050291)
文摘The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established.
基金Project(61203021)supported by the National Natural Science Foundation of ChinaProject(2011216011)supported by the Scientific and Technological Program of Liaoning Province,China+2 种基金Project(2013020024)supported by the Natural Science Foundation of Liaoning Province,ChinaProject(2012BAF05B00)supported by the National Science and Technology Support Program,ChinaProject(LJQ2015061)supported by the Program for Liaoning Excellent Talents in Universities,China
文摘The control of gas fractionation unit(GFU) in petroleum industry is very difficult due to multivariable characteristics and a large time delay.PID controllers are still applied in most industry processes.However,the traditional PID control has been proven not sufficient and capable for this particular petro-chemical process.In this work,an incremental multivariable predictive functional control(IMPFC) algorithm was proposed with less online computation,great precision and fast response.An incremental transfer function matrix model was set up through the step-response data,and predictive outputs were deduced with the theory of single-value optimization.The results show that the method can optimize the incremental control variable and reject the constraint of the incremental control variable with the positional predictive functional control algorithm,and thereby making the control variable smoother.The predictive output error and future set-point were approximated by a polynomial,which can overcome the problem under the model mismatch and make the predictive outputs track the reference trajectory.Then,the design of incremental multivariable predictive functional control was studied.Simulation and application results show that the proposed control strategy is effective and feasible to improve control performance and robustness of process.
文摘The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method.
文摘Reaction control system(RCS) is a powerful and efficient actuator for space vehicles attitude control, which is typically characterized as a pulsed unilateral effector only with two states(off/on). Along with inevitable internal uncertainties and external disturbances in practice, this inherent nonlinear character always hinders space vehicles autopilot from pursuing precise tracking performance. Compared to most of pre-existing methodologies that passively suppress the uncertainties and disturbances, a design based on predictive functional control(PFC) and generalized extended state observer(GESO) is firstly proposed for three-axis RCS control system to actively reject that with no requirement for additional fuel consumption. To obtain a high fidelity predictive model on which the performance of PFC greatly depends, the nonlinear coupling multiple-input multiple-output(MIMO) flight dynamics model is parameterized as a state-dependent coefficient form. And based on that, a MIMO PFC algorithm in state space domain for a plant of arbitrary orders is deduced in this paper.The internal uncertainties and external disturbances are lumped as a total disturbance, which is estimated and cancelled timely to further enhance the robustness. The continuous control command synthesised by above controller-rejector tandem is finally modulated by pulse width pulse frequency modulator(PWPF) to on-off signals to meet RCS requirement. The robustness and feasibility of the proposed design are validated by a series of performance comparison simulations with some prominent methods in the presence of significant perturbations and disturbances, as well as measurement noise.
基金the Natural Science Foundation of Zhejiang Province,China (Y105141)Technological Project of Zhejiang Education Department,China (20050291).
文摘A method is developed by which control Lyapunov functions of a class of nonlinear systems can be constructed systematically. Based on the control Lyapunov function, a feedback control is obtained to stabilize the closed-loop system. In addition, this method is applied to stabilize the Benchmark system. A simulation shows the effectiveness of the method.
基金the Natural Science Foundation of China (60774011)the Natural ScienceFoundation of Zhejiang Province in China (Y105141)
文摘The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.
基金Project(2007AA04Z162) supported by the National High-Tech Research and Development Program of ChinaProjects(2006T089, 2009T062) supported by the University Innovation Team in the Educational Department of Liaoning Province, China
文摘In order to obtain accurate prediction model and compensate for the influence of model mismatch on the control performance of the system and avoid solving nonlinear programming problem,an adaptive fuzzy predictive functional control(AFPFC) scheme for multivariable nonlinear systems was proposed.Firstly,multivariable nonlinear systems were described based on Takagi-Sugeno(T-S) fuzzy models;assuming that the antecedent parameters of T-S models were kept,the consequent parameters were identified on-line by using the weighted recursive least square(WRLS) method.Secondly,the identified T-S models were linearized to be time-varying state space model at each sampling instant.Finally,by using linear predictive control technique the analysis solution of the optimal control law of AFPFC was established.The application results for pH neutralization process show that the absolute error between the identified T-S model output and the process output is smaller than 0.015;the tracking ability of the proposed AFPFC is superior to that of non-AFPFC(NAFPFC) for pH process without disturbances,the overshoot of the effluent pH value of AFPFC with disturbances is decreased by 50% compared with that of NAFPFC;when the process parameters of AFPFC vary with time the integrated absolute error(IAE) performance index still retains to be less than 200 compared with that of NAFPFC.
基金Supported by National Natural Science Foundation of P. R. China (60572070, 60325311, 60534010) Natural Science Foundation of Liaoning Province (20022030)
文摘The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature. First, the so-called stochastic LaSalle theory is extended to some extent, and accordingly, the results of global ultimate boundedness for stochastic nonlinear systems are developed. Next, a new design scheme of fuzzy adaptive control is proposed. The advantage of it is that it does not require priori knowledge of virtual control gain function sign, which is usually demanded in many designs. At the same time, the track performance of closed-loop systems is improved by adaptive modifying the estimated error upper bound. By theoretical analysis, the signals of closed-loop systems are globally ultimately bounded in probability and the track error converges to a small residual set around the origin in 4th-power expectation.
基金supported by the National Natural Science Fundation of China(61273127)the Specialized Research Fund of the Doctoral Program in Higher Education(20106118110009+2 种基金20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(12JK0524)the Young Teachers Scientific Research Fund of Xi’an University of Posts and Telecommunications(1100434)
文摘A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.
文摘In this paper, adaptive identification and control of nonlinear dynamical systems are investigated using radial basis function networks (RBF). Firstly, a novel approach to train the RBF is introduced, which employs an adaptive fuzzy generalized learning vector quantization (AFGLVQ) technique and recursive least squares algorithm with variable forgetting factor (VRLS). The AFGLVQ adjusts the centers of the RBF while the VRLS updates the connection weights of the network. The identification algorithm has the properties of rapid convergence and persistent adaptability that make it suitable for real-time control. Secondly, on the basis of the one-step ahead RBF predictor, the control law is optimized iteratively through a numerical stable Davidon's least squares-based (SDLS) minimization approach. Four nonlinear examples are simulated to demonstrate the effectiveness of the identification and control algorithms.
文摘The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding Legendre series. Matching the first three terms of the Legendre series of the loop gain with the desired one gives the PID controller parameters. The closed loop system stability conditions in terms of the Legendre basis function pole(λ) for a wide range of systems including the first order, second order, double integrator, first order plus dead time, and first order unstable plants are obtained. For first order and double integrator plants, the closed loop system stability is preserved for all values of λ and for the other plants, an appropriate range in terms of λ is obtained. The optimum value of λ to attain a minimum integral square error performance index in the presence of the control signal constraints is achieved. The numerical simulations demonstrate the benefits of the Legendre based PID controller.
基金Supported by National Basic Research Program of China（973 Program）（2013CB035500） National Natural Science Foundation of China（61233004,61221003,61074061）+1 种基金 International Cooperation Program of Shanghai Science and Technology Commission （12230709600） the Higher Education Research Fund for the Doctoral Program of China（20120073130006）
基金supported by the China Postdoctoral Science Foundation (200904501035 201003548)+3 种基金the National Natural Science Foundation of China (60835001907160289101600460804017)
文摘An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network （FTRBFNN） is presented for a general class of strict-feedback nonlinear systems,which may possess a wide class of uncertainties that are not linearly parameterized and do not have any prior knowledge of the bounding functions.FTRBFNN is employed to approximate the uncertainty online,and a systematic framework for adaptive controller design is given by dynamic surface control. The control algorithm has two outstanding features,namely,the neural network regulates the weights,width and center of Gaussian function simultaneously,which ensures the control system has perfect ability of restraining different unknown uncertainties and the integral term of tracking error introduced in the control law can eliminate the static error of the closed loop system effectively. As a result,high control precision can be achieved.All signals in the closed loop system can be guaranteed bounded by Lyapunov approach.Finally,simulation results demonstrate the validity of the control approach.
基金supported by the National Natural Science Foundation of China (9071602860974106)
文摘The control law design for a near-space hypersonic vehicle（NHV） is highly challenging due to its inherent nonlinearity,plant uncertainties and sensitivity to disturbances.This paper presents a novel functional link network（FLN） control method for an NHV with dynamical thrust and parameter uncertainties.The approach devises a new partially-feedback-functional-link-network（PFFLN） adaptive law and combines it with the nonlinear generalized predictive control（NGPC） algorithm.The PFFLN is employed for approximating uncertainties in flight.Its weights are online tuned based on Lyapunov stability theorem for the first time.The learning process does not need any offline training phase.Additionally,a robust controller with an adaptive gain is designed to offset the approximation error.Finally,simulation results show a satisfactory performance for the NHV attitude tracking,and also illustrate the controller＇s robustness.
文摘大豆分离蛋白(Soy Protein Isolate,SPI)功能特性决定应用领域,加工过程中NaOH添加量影响SPI功能特性。文章究利用Matlab模拟,采用传统比例积分微分(proportional integral derivative,PID)和模糊自适应控制(Adaptive Fuzzy Control,AFC)方法调控NaOH,中和大豆凝乳,并分析其对SPI结构和功能特性的影响。结果表明,pH值为7时,常规PID控制方法NaOH超调量为1.86%,调节时间为47.1 s;模糊自适应控制方法无超调量,调节时间为35.8 s。模糊自适应控制下,SPI傅里叶红外光谱吸收峰更稳定,紫外吸收特性更佳,二级结构向有序转变,表面疏水性较高,且溶解性、起泡性、泡沫稳定性、乳化性和乳化稳定性均优于常规PID控制方法。
