scholarly journals Lyapunov Control of Quantum Systems with Impulsive Control Fields

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Wei Yang ◽  
Jitao Sun
Keyword(s):  
Lyapunov Functions ◽  
Control Method ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Quantum Systems ◽  
Impulsive Systems ◽  
Finite Dimensional ◽  
Lyapunov Control ◽  
Control Of Quantum Systems ◽  
Invariant Principle

We investigate the Lyapunov control of finite-dimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method.

scholarly journals Finite-Time Lyapunov Functions and Impulsive Control Design

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Huijuan Li ◽  
Qingxia Ma
Keyword(s):  
Finite Time ◽  
Lyapunov Functions ◽  
Lorenz System ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Impulsive Systems ◽  
Lyapunov Theorem ◽  
The Lorenz System ◽  
The Stability

In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to the results, we design an impulsive controller for a chaotic system modified from the Lorenz system.

ON IMPULSIVE CONTROL AND ITS APPLICATION TO CHEN'S CHAOTIC SYSTEM

2002 ◽  
Vol 12 (05) ◽  
pp. 1191-1197 ◽  
Author(s):  
ZHI-HONG GUAN ◽  
RUI-QUAN LIAO ◽  
FENG ZHOU ◽  
HUA O. WANG
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Chaotic System ◽  
Control Method ◽  
Impulsive Control ◽  
Asymptotical Stability ◽  
Impulsive Systems ◽  
Chaotic State ◽  
Chaos Suppression ◽  
Zero Equilibrium

In this paper, impulsive control of nonlinear systems and its application to Chen's chaotic system are considered. A new impulsive control method for chaos suppression, using Chen's system as an example, is developed. Some new general criteria for exponential stability and asymptotical stability of nonlinear impulsive systems are established and, particularly, some simple conditions sufficient for driving the chaotic state of Chen's system to its zero equilibrium are presented.

scholarly journals Rapid Lyapunov control of finite-dimensional quantum systems

Automatica ◽  
2017 ◽  
Vol 81 ◽  
pp. 164-175 ◽  
Author(s):  
Sen Kuang ◽  
Daoyi Dong ◽  
Ian R. Petersen
Keyword(s):  
Quantum Systems ◽  
Finite Dimensional ◽  
Lyapunov Control

scholarly journals Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Kexue Zhang ◽  
Xinzhi Liu
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Discrete Systems ◽  
Impulsive Systems ◽  
Uniform Asymptotic Stability ◽  
Stability And Instability ◽  
Special Cases ◽  
Two Measures

We investigate some stability problems in terms of two measures for nonlinear dynamic systems on time scales with fixed moments of impulsive effects. Sufficient conditions for (uniform) stability, (uniform) asymptotic stability, and instability in terms of two measures are derived by using the method of Lyapunov functions. Our results include the existing results as special cases when the time scale reduces to the set of real numbers. Particularly, our results provide stability criteria for impulsive discrete systems in terms of two measures, which have not been investigated extensively. Two examples are presented to illustrate the efficiency of the proposed results.

Stability analysis of hybrid neural networks with impulsive time window

2016 ◽  
Vol 10 (01) ◽  
pp. 1750011 ◽  
Author(s):  
Xin Wang ◽  
Hui Wang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Lyapunov Functions ◽  
Impulsive Control ◽  
Time Window ◽  
Control Strategies ◽  
Urgent Problem ◽  
Impulsive Systems ◽  
Random Manner ◽  
New Challenges ◽  
Hybrid Neural Networks

The urgent problem with impulsive moments cannot be determined in advance brings new challenges beyond the conventional impulsive systems theory. In order to solve this problem, in this paper, a novel class of system with impulsive time window is proposed. Different from the conventional impulsive control strategies, the main characteristic of the impulsive time window is that impulse occurs in a random manner. Moreover, for the importance of the hybrid neural networks, using switching Lyapunov functions and a generalized Hanlanay inequality, some general criteria for asymptotic and exponential stability of the hybrid neural networks with impulsive time window are established. Finally, some simulations are provided to further illustrate the effectiveness of the results.

scholarly journals Leader-Following Consensus of Multiagent Systems with Time-Varying Delays via Impulsive Control

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhiyong Ye ◽  
Yungen Chen ◽  
Hua Zhang
Keyword(s):  
Multiagent Systems ◽  
Control Method ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Distributed Consensus ◽  
Consensus Protocol ◽  
Sample Data ◽  
Leader Following ◽  
Discrete Moments

The leader-following consensus problem for delayed multiagent systems is investigated over stochastic switching topologies via impulsive control method. A distributed consensus protocol is proposed based on sample data information. The convergence analysis for such algorithm over undirected and directed networks is provided, and some sufficient conditions to guarantee the consensus are also established. It is shown that delayed networks can achieve consensus even information is exchanged among followers just at some discrete moments. At last, some numerical examples are given to illustrate the effectiveness of the proposed protocols.

scholarly journals Impulsive Synchronization and Adaptive-Impulsive Synchronization of a Novel Financial Hyperchaotic System

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xiuli Chai ◽  
Zhihua Gan ◽  
Chunxiao Shi
Keyword(s):  
Dynamical Systems ◽  
Impulsive Control ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Hyperchaotic System ◽  
Impulsive Synchronization ◽  
Control Scheme ◽  
Functional Differential ◽  
Invariant Principle

The impulsive synchronization and adaptive-impulsive synchronization of a novel financial hyperchaotic system are investigated. Based on comparing principle for impulsive functional differential equations, several sufficient conditions for impulsive synchronization are derived, and the upper bounds of impulsive interval for stable synchronization are estimated. Furthermore, a nonlinear adaptive-impulsive control scheme is designed to synchronize the financial system using invariant principle of impulsive dynamical systems. Moreover, corresponding numerical simulations are presented to illustrate the effectiveness and feasibility of the proposed methods.

scholarly journals A Quantum System Control Method Based on Enhanced Reinforcement Learning

2021 ◽  
Author(s):  
Wenjie Liu ◽  
Bosi Wang ◽  
Jihao Fan ◽  
Yebo Ge ◽  
Mohammed Zidan
Keyword(s):  
Reinforcement Learning ◽  
Quantum System ◽  
Control Method ◽  
Quantum Systems ◽  
System Control ◽  
Control Task ◽  
Initial State ◽  
Simulation Experiments ◽  
Switch Control ◽  
Control Of Quantum Systems

Abstract The design of quantum system control is a key task to a powerful quantum information technology. In practical, traditional quantum system control methods often face different constraints, and are easy to cause both leakage and stochastic control errors under the condition of limited resources. Reinforcement learning has been proved as an efficient way to complete the quantum system control task. So a quantum system control method based on enhanced reinforcement learning (QSC-ERL) is proposed. A satisfactory control strategy is obtained through enhanced reinforcement learning so that the quantum system can be evolved accurately from the initial state to the target state. According to the number of candidate unitary operations, the three-switch control is used for simulation experiments. Compared with other methods, the QSC-ERL can achieve high fidelity learning control of quantum systems and improve the efficiency of quantum system control.

FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA NONLINEAR ADAPTIVE–IMPULSIVE CONTROL

2011 ◽  
Vol 22 (11) ◽  
pp. 1281-1291 ◽  
Author(s):  
RANCHAO WU ◽  
DONGXU CAO
Keyword(s):  
Numerical Simulation ◽  
Dynamical Systems ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Simulation Results ◽  
Invariant Principle

In this paper, function projective synchronization of chaotic systems is investigated through nonlinear adaptive–impulsive control. To achieve synchronization, suitable nonlinear continuous and impulsive controllers are designed, according to invariant principle of impulsive dynamical systems. Sufficient conditions are given to ensure the synchronization. Numerical simulation results show the effectiveness of the proposed scheme.

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