This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.S...This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given.展开更多
We consider the topological behaviors of continuous maps with one topological attractor on compact metric space X.This kind of map is a generalization of maps such as topologically expansive Lorenz map,unimodal map wi...We consider the topological behaviors of continuous maps with one topological attractor on compact metric space X.This kind of map is a generalization of maps such as topologically expansive Lorenz map,unimodal map without homtervals and so on.Under the finiteness and basin conditions,we provide a leveled A-R pair decomposition for such maps,and characterize α-limit set of each point.Based on weak Morse decomposition of X,we construct a bounded Lyapunov function V(x),which gives a clear description of orbit behavior of each point in X except a meager set.展开更多
This paper investigates the chaos synchronisation between two coupled chaotic Chua＇s circuits. The sufficient condition presented by linear matrix inequalities （LMIs） of global asymptotic synchronisation is attaine...This paper investigates the chaos synchronisation between two coupled chaotic Chua＇s circuits. The sufficient condition presented by linear matrix inequalities （LMIs） of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions （pwLDIs） model of synchronisation error dynamics, then we design a switching （piecewise-linear） feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results.展开更多
For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively prov...For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization： a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.展开更多
In this paper we consider general nonlinear switching systems. Under an additional assumption, we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense.
In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities ...In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities （LMIs） by constructing new Lyapunov-Krasovskii functional. The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints. The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound. Numerical examples are presented to show the effectiveness of the proposed method.展开更多
针对机械臂在运行过程中因输入输出受限、外界未知干扰以及自身动力学参数不确定性导致控制精度低和抗干扰能力差的问题,提出基于时变正切型障碍李雅普诺夫函数的自适应反步滑模控制方法(adaptive backstepping sliding mode control fo...针对机械臂在运行过程中因输入输出受限、外界未知干扰以及自身动力学参数不确定性导致控制精度低和抗干扰能力差的问题,提出基于时变正切型障碍李雅普诺夫函数的自适应反步滑模控制方法(adaptive backstepping sliding mode control for time-varying tangent barrier Lyapunov,TTBLF-ABSMC)。首先,通过设计饱和补偿系统解决输入受限问题,提高控制系统的稳定性;其次,将外界未知干扰与自身动力学参数不确定性视为复合干扰,设计反馈自适应律对其做出准确估计;同时,采用时变正切型障碍李雅普诺夫函数将位置误差和速度误差限制在时变范围内;最后,通过李雅普诺夫理论分析证明闭环控制系统是有界稳定的。仿真实验结果表明:与采取时变对数型障碍李雅普诺夫函数的控制方法相比,该控制方法使机械臂关节1、2的跟踪误差分别降低了58%、33%;相比于未考虑输入受限方法,该控制方法在关节1、2的轨迹跟踪响应速度分别提升了69%、50%,有效的提高了系统的控制精度和抗干扰能力。展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.62176140)。
文摘This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given.
基金supported by the National Key Re-search and Development Program of China(2020YFA0714200)supported by the Excellent Dissertation Cultivation Funds of Wuhan University of Technology(2018-YS-077)。
文摘We consider the topological behaviors of continuous maps with one topological attractor on compact metric space X.This kind of map is a generalization of maps such as topologically expansive Lorenz map,unimodal map without homtervals and so on.Under the finiteness and basin conditions,we provide a leveled A-R pair decomposition for such maps,and characterize α-limit set of each point.Based on weak Morse decomposition of X,we construct a bounded Lyapunov function V(x),which gives a clear description of orbit behavior of each point in X except a meager set.
基金Project partially supported by the grant from the Research Grants Council of the Hong Kong Special Administrative Region,China (Grant No. 101005)the National Natural Science Foundation of China (Grant No. 60904004)the Key Youth Science and Technology Foundation of University of Electronic Science and Technology of China (Grant No. L08010201JX0720)
文摘This paper investigates the chaos synchronisation between two coupled chaotic Chua＇s circuits. The sufficient condition presented by linear matrix inequalities （LMIs） of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions （pwLDIs） model of synchronisation error dynamics, then we design a switching （piecewise-linear） feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results.
基金Project supported by the National Basic Research Program of China(Grant No.2010CB529200)the National Natural Science Foundation of China(Grant Nos.61073087 and 91029738)
文摘For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization： a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.
基金Supported by the NSF of Commission of Education of Henan Province(200510459002)
文摘In this paper we consider general nonlinear switching systems. Under an additional assumption, we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense.
基金Project supported by the Daegu University Research Grant,2009
文摘In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities （LMIs） by constructing new Lyapunov-Krasovskii functional. The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints. The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound. Numerical examples are presented to show the effectiveness of the proposed method.
文摘针对机械臂在运行过程中因输入输出受限、外界未知干扰以及自身动力学参数不确定性导致控制精度低和抗干扰能力差的问题,提出基于时变正切型障碍李雅普诺夫函数的自适应反步滑模控制方法(adaptive backstepping sliding mode control for time-varying tangent barrier Lyapunov,TTBLF-ABSMC)。首先,通过设计饱和补偿系统解决输入受限问题,提高控制系统的稳定性;其次,将外界未知干扰与自身动力学参数不确定性视为复合干扰,设计反馈自适应律对其做出准确估计;同时,采用时变正切型障碍李雅普诺夫函数将位置误差和速度误差限制在时变范围内;最后,通过李雅普诺夫理论分析证明闭环控制系统是有界稳定的。仿真实验结果表明:与采取时变对数型障碍李雅普诺夫函数的控制方法相比,该控制方法使机械臂关节1、2的跟踪误差分别降低了58%、33%;相比于未考虑输入受限方法,该控制方法在关节1、2的轨迹跟踪响应速度分别提升了69%、50%,有效的提高了系统的控制精度和抗干扰能力。
