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
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
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
An improved model predictive control algorithm is proposed for Hammerstein-Wiener nonlinear systems.The proposed synthesis algorithm contains two parts:offline design the polytopic invariant sets,and online solve the ...An improved model predictive control algorithm is proposed for Hammerstein-Wiener nonlinear systems.The proposed synthesis algorithm contains two parts:offline design the polytopic invariant sets,and online solve the min-max optimization problem.The polytopic invariant set is adopted to replace the traditional ellipsoid invariant set.And the parameter-correlation nonlinear control law is designed to replace the traditional linear control law.Consequently,the terminal region is enlarged and the control effect is improved.Simulation and experiment are used to verify the validity of the wind tunnel flow field control algorithm.展开更多
Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approa...Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approach, the maximum and minimum of partial derivative for input and output nonlinearities are solved in the neighbourhood of the equilibrium. And several parameter-dependent Lyapunov functions, each one corresponding to a different vertex of polytopic descriptions models, are introduced to analyze the stability of Hammerstein-Wiener systems, but only one Lyapunov function is utilized to analyze system stability like the traditional method. Consequently, the conservation of the traditional quadratic stability is removed, and the terminal regions are enlarged. Simulation and field trial results show that the proposed algorithm is valid. It has higher control precision and shorter blowing time than the traditional approach.展开更多
The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function （CLF）, a sufficient and necessary condition for Lyapunov stabilization is given. From ...The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function （CLF）, a sufficient and necessary condition for Lyapunov stabilization is given. From the condition, several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.展开更多
This paper proposes a fast integral terminal sliding mode（ITSM） control method for a cascaded nonlinear dynamical system with mismatched uncertainties. Firstly, an integral terminal sliding mode surface is presented...This paper proposes a fast integral terminal sliding mode（ITSM） control method for a cascaded nonlinear dynamical system with mismatched uncertainties. Firstly, an integral terminal sliding mode surface is presented, which not only avoids the singularity in the traditional terminal sliding mode, but also addresses the mismatched problems in the nonlinear control system. Secondly, a new ITSM controller with finite convergence time based on the backstepping technique is derived for a cascaded nonlinear dynamical system with mismatched uncertainties. Thirdly, the convergence time of ITSM is analyzed, whose convergence speed is faster than those of two nonsingular terminal sliding modes.Finally, simulation results are presented in order to evaluate the effectiveness of ITSM control strategies for mismatched uncertainties.展开更多
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
The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are...The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are bounded, but the upper bounds are incompletely known. This paper can be viewed as an extension of the work in reference [1]. To compensate the uncertainties, an adaptive robust controller based on Lyapunov method is proposed and the design algorithm is also suggested. Compared with some previous controllers which can only ensure ultimate uniform boundedness of the systems, the controller given in the paper can make sure that the obtained closed-loop system is asymptotically stable in the large. Simulations show that the method presented is available and effective.展开更多
An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov fu...An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF) techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.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 robust adaptive control is proposed for a class of uncertain nonlinear non-affine SISO systems. In order to approximate the unknown nonlinear function, an affine type neural network(ATNN) and neural state feedback c...A robust adaptive control is proposed for a class of uncertain nonlinear non-affine SISO systems. In order to approximate the unknown nonlinear function, an affine type neural network(ATNN) and neural state feedback compensation are used, and then to compensate the approximation error and external disturbance, a robust control term is employed. By Lyapunov stability analysis for the closed-loop system, it is proven that tracking errors asymptotically converge to zero. Moreover, an observer is designed to estimate the system states because all the states may not be available for measurements. Furthermore, the adaptation laws of neural networks and the robust controller are given based on the Lyapunov stability theory. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed control method. Finally, two simulation examples show that the proposed method exhibits strong robustness, fast response and small tracking error, even for the non-affine nonlinear system with external disturbance, which confirms the effectiveness of the proposed approach.展开更多
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
In this paper, an indirect adaptive fuzzy output feedback controller with supervisory mode for a class of unknown nonlinear systems is developed. The proposed approach does not need the availability of the state varia...In this paper, an indirect adaptive fuzzy output feedback controller with supervisory mode for a class of unknown nonlinear systems is developed. The proposed approach does not need the availability of the state variables, moreover, a supervisory controller is appended to the adaptive fuzzy controller to force the state to be within the constraint set. Therefore, if the adaptive fuzzy controller cannot maintain the stability, the supervisory controller starts to work to guarantee stability. On the other hand, if the adaptive fuzzy controller works well, the supervisory controller will be de-activated. The overall adaptive fuzzy control scheme guarantees the stability of the whole closed-loop systems. The simulation results confirm the effectiveness of the proposed method.展开更多
The back-stepping designs based on confine functions are suggested for the robust output-feedback global stabilization of a class of nonlinear continuous systems; the proposed stabilizer is efficient for the nonlinear...The back-stepping designs based on confine functions are suggested for the robust output-feedback global stabilization of a class of nonlinear continuous systems; the proposed stabilizer is efficient for the nonlinear continuous systems confined by a bound function, the nonlinearities of the systems may be of varied forms or uncertain; the designed stabilizer is robust means that a class of nonlinear continuous systems can be stabilized by the same output feedback stabilization schemes; numerical simulation examples are given.展开更多
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Project(61074074)supported by the National Natural Science Foundation,ChinaProject(KT2012C01J0401)supported by the Group Innovation Fund,China
文摘An improved model predictive control algorithm is proposed for Hammerstein-Wiener nonlinear systems.The proposed synthesis algorithm contains two parts:offline design the polytopic invariant sets,and online solve the min-max optimization problem.The polytopic invariant set is adopted to replace the traditional ellipsoid invariant set.And the parameter-correlation nonlinear control law is designed to replace the traditional linear control law.Consequently,the terminal region is enlarged and the control effect is improved.Simulation and experiment are used to verify the validity of the wind tunnel flow field control algorithm.
基金Project(61074074) supported by the National Natural Science Foundation,ChinaProject(KT2012C01J0401) supported by the Group Innovative Fund,China
文摘Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approach, the maximum and minimum of partial derivative for input and output nonlinearities are solved in the neighbourhood of the equilibrium. And several parameter-dependent Lyapunov functions, each one corresponding to a different vertex of polytopic descriptions models, are introduced to analyze the stability of Hammerstein-Wiener systems, but only one Lyapunov function is utilized to analyze system stability like the traditional method. Consequently, the conservation of the traditional quadratic stability is removed, and the terminal regions are enlarged. Simulation and field trial results show that the proposed algorithm is valid. It has higher control precision and shorter blowing time than the traditional approach.
基金This project was supported by the National Natural Science Foundation of Fujian province (A0510025) .
文摘The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function （CLF）, a sufficient and necessary condition for Lyapunov stabilization is given. From the condition, several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.
基金supported by the National Natural Science Foundation of China(61473226)
文摘This paper proposes a fast integral terminal sliding mode（ITSM） control method for a cascaded nonlinear dynamical system with mismatched uncertainties. Firstly, an integral terminal sliding mode surface is presented, which not only avoids the singularity in the traditional terminal sliding mode, but also addresses the mismatched problems in the nonlinear control system. Secondly, a new ITSM controller with finite convergence time based on the backstepping technique is derived for a cascaded nonlinear dynamical system with mismatched uncertainties. Thirdly, the convergence time of ITSM is analyzed, whose convergence speed is faster than those of two nonsingular terminal sliding modes.Finally, simulation results are presented in order to evaluate the effectiveness of ITSM control strategies for mismatched uncertainties.
基金Project(51005253) supported by the National Natural Science Foundation of ChinaProject(2007AA04Z344) supported by the National High Technology Research and Development Program of China
文摘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.
基金Supported by National Natural Science Foundation of China （60774011, 60674024）, Natural Science Foundation of Zhejiang Province （Y105141）, and Natural Science Foundation of Fujian Province （2008J0026）
文摘The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are bounded, but the upper bounds are incompletely known. This paper can be viewed as an extension of the work in reference [1]. To compensate the uncertainties, an adaptive robust controller based on Lyapunov method is proposed and the design algorithm is also suggested. Compared with some previous controllers which can only ensure ultimate uniform boundedness of the systems, the controller given in the paper can make sure that the obtained closed-loop system is asymptotically stable in the large. Simulations show that the method presented is available and effective.
文摘An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF) techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.
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Project(61433004)suppouted by the National Natural Science Foundation of China
文摘A robust adaptive control is proposed for a class of uncertain nonlinear non-affine SISO systems. In order to approximate the unknown nonlinear function, an affine type neural network(ATNN) and neural state feedback compensation are used, and then to compensate the approximation error and external disturbance, a robust control term is employed. By Lyapunov stability analysis for the closed-loop system, it is proven that tracking errors asymptotically converge to zero. Moreover, an observer is designed to estimate the system states because all the states may not be available for measurements. Furthermore, the adaptation laws of neural networks and the robust controller are given based on the Lyapunov stability theory. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed control method. Finally, two simulation examples show that the proposed method exhibits strong robustness, fast response and small tracking error, even for the non-affine nonlinear system with external disturbance, which confirms the effectiveness of the proposed approach.
基金Supported by National Natural Science Foundation of China （60774010）, Program for New Century Excellent Talents in University of China （NCET-05-0607）, Program for Summit of Six Types of Talents of Jiangsu Province （07-A-020）, and Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province （07KJB510114）
文摘适应州反馈的稳定为在的高顺序的随机的非线性的系统的一个类被调查函数 fi 的上面的界限(?? 铄吗？？
文摘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.
基金Supported by National Natural Science Foundation of P. R. China (60274019)National Key Basic Research and Development Program of P. R. China (2002CB312200)
文摘In this paper, an indirect adaptive fuzzy output feedback controller with supervisory mode for a class of unknown nonlinear systems is developed. The proposed approach does not need the availability of the state variables, moreover, a supervisory controller is appended to the adaptive fuzzy controller to force the state to be within the constraint set. Therefore, if the adaptive fuzzy controller cannot maintain the stability, the supervisory controller starts to work to guarantee stability. On the other hand, if the adaptive fuzzy controller works well, the supervisory controller will be de-activated. The overall adaptive fuzzy control scheme guarantees the stability of the whole closed-loop systems. The simulation results confirm the effectiveness of the proposed method.
基金Supported by National Natural Science Foundation of China （60674036）, the Science and Technical Development Plan of Shandong Province （2004GG4204014）, the Program for New Century Excellent Talents in University of China （NCET-07-0513）, the Key Science and Technique Foundation of Ministry of Education of China （108079）, and the Excellent Young and Middle-aged Scientist Award of Shandong Province of China （2007BS01010）
基金Supported by National Natural Science Foundation of China（60774010 10971256） Natural Science Foundation of Jiangsu Province（BK2009083）+1 种基金 Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province（07KJB510114） Shandong Provincial Natural Science Foundation of China（ZR2009GM008 ZR2009AL014）
基金Supported by National Natural Science Foundations of China （61325016, 61273084, 61233014）, Natural Science Foundation for Distinguished Young Scholar of Shandong Province of China （JQ200919）, and the Independent Innovation Foundation of Shan- dong University （2012JC014）
基金This project was supported by the National Natural Science Foundation of China(69974017 60274020 60128303)
文摘The back-stepping designs based on confine functions are suggested for the robust output-feedback global stabilization of a class of nonlinear continuous systems; the proposed stabilizer is efficient for the nonlinear continuous systems confined by a bound function, the nonlinearities of the systems may be of varied forms or uncertain; the designed stabilizer is robust means that a class of nonlinear continuous systems can be stabilized by the same output feedback stabilization schemes; numerical simulation examples are given.
