Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems

This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discretetime chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.     

一类不确定离散混沌系统的自抗扰控制器与小脑神经网络并行优化控制

针对一类受扰不确定离散非线性混沌系统,提出了基于免疫动态微粒群优化策略的ADRC与CMAC神经网络并行控制方法(ADRC-CMAC).ADRC控制器抑制系统扰动,保证系统的稳定性;CMAC神经网络控制器实现前馈控制保证系统的控制精度和响应速度.利用动态免疫微粒群算法对ADRC-CMAC并行控制器参数进行全局优化.实验结果表明该控制方法具有较快系统的响应速度,较好的抗干扰能力,控制精度高. 关键词： 自抗扰控制器 小脑神经网络 并行控制 混沌系统     

A nonlinear control scheme to anticipated and complete synchronization in discrete-time chaotic (hyperchaotic) systems

In this Letter, a new synchronization scheme is presented to study anticipated synchronization and complete synchronization in discrete-time chaotic and hyperchaotic systems based on the active control idea. The scheme is applied to investigate anticipated synchronization and complete synchronization between two identical 3D generalized Hénon maps, as well as 3D discrete-time Yeh–Kokotovic map and 3D generalized Hénon maps. Numerical simulations are used to verify the effectiveness of the proposed scheme.     

The variable, fractional-order discrete-time PD controller in the IISv1.3 robot arm control

In this paper, the discrete differentiation order functions of the variable, fractional-order PD controller (VFOPD) are considered. In the proposed VFOPD controller, a variable, fractional-order backward difference is applied to perform closed-loop, system error, discrete-time differentiation. The controller orders functions which may be related to the controller input or output signal or an input and output signal. An example of the VFOPD controller is applied to the robot arm closed-loop control due to system changes in moment of inertia. The close-loop system step responses are presented.     

Q-S (complete or anticipated) synchronization backstepping scheme in a class of discrete-time chaotic (hyperchaotic) systems: a symbolic-numeric computation approach

First, a type of Q-S (complete or anticipated) synchronization is defined in discrete-time dynamical systems. Second, based on backstepping design with a scalar controller, a systematic, concrete and automatic scheme is presented to investigate Q-S (complete or anticipated) synchronization between the discrete-time drive system and response system with strict-feedback form. Finally, the proposed scheme is used to illustrate Q-S (complete or anticipated) synchronization between the two-dimensional discrete-time Lorenz system and Fold system, as well as the three-dimensional hyperchaotic discrete-time Rossler system and generalized discrete-time Rossler system. Moreover numerical simulations are used to verify the effectiveness of the proposed scheme. Our scheme can be also extended to investigate Q-S (complete or anticipated) synchronization between other discrete-time dynamical systems with strict-feedback forms. With the aid of symbolic-numeric computation, the scheme can be performed to yield automatically the scalar controller and to verify its effectiveness in computer.     

Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.     

一类离散时间广义系统的迭代学习控制

针对一类离散时间广义系统,提出了一种离散迭代学习控制算法.首先,通过非奇异变换将离散时间广义系统分解为正常离散状态方程和代数方程的形式.然后,利用上一次迭代学习获得的前一时刻误差和当前时刻误差来修正上一次的控制量,从而获得下一次迭代学习的新控制量,并对算法的收敛性进行了理论证明,给出了算法收敛的充分条件.研究结果表明,所提算法能够在有限时间区间内实现系统状态对期望状态的完全跟踪.最后,通过仿真算例进一步验证了所提算法的有效性.     

Q-S synchronization in 3D Hénon-like map and generalized Hénon map via a scalar controller

In this Letter, a generalized, systematic and automatic backstepping scheme is developed to investigate the Q-S synchronization of two identical 3D discrete-time dynamical systems and two different 3D discrete-time dynamical systems. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate chaos synchronization between two identical 3D generalized Hénon map and Q-S synchronization between two different 3D generalized Hénon map and Hénon-like map via a scalar controller, respectively. Moreover numerical simulations are used to verify the effectiveness of the proposed scheme. In addition, the scheme can be also applied to investigate the tracking problem in the discrete-time systems and to generate automatically the scalar controller in computer with the aid of symbolic-numeric computation.     

Prediction-based control of chaos

Pyragas proposes a practically useful control method, called delayed feedback control, for control of chaos. Conditions for (local) stabilization by the delayed feedback control, however, are more restricted than those by the OGY method. In order to overcome this problem, we propose a novel control method, called a prediction-based feedback control, for discrete-time chaotic systems. Moreover, we give necessary and sufficient conditions for exponential stabilization of fixed points by the proposed method.     

Controllability of Discrete-Time Multi-Agent Systems with Multiple Leaders on Fixed Networks

This paper investigates controllability of discrete-time multi-agent systems with multiple leaders on fixed networks. The leaders are particular agents playing a part in external inputs to steer other member agents. The followers can arrive at any predetermined configuration by regulating the behaviors of the leaders. Some sufficient and necessary conditions are proposed for the controllability of discrete-time multi-agent systems with multiple leaders. Moreover, the case with isolated agents is discussed. Numerical examples and simulations are proposed to illustrate the theoretical results we established.     

Controllability of Discrete-Time Multi-Agent Systems with Multiple Leaders on Fixed Networks

This paper investigates controllability of discrete-time multi-agent systems with multiple leaders on fixed networks. The leaders are particular agents playing a part in external inputs to steer other member agents. The followers can arrive at any predetermined configuration by regulating the behaviors of the leaders. Some sufficient and necessary conditions are proposed for the controllability of discrete-time multi-agent systems with multiple leaders. Moreover, the case with isolated agents is discussed. Numerical examples and simulations are proposed to illustrate the theoretical results we established.     

A discrete-time chaos synchronization system for electronic locking devices

This paper presents a novel electronic locking key based on discrete-time chaos synchronization. Two Chen chaos generators are synchronized using the Model-Matching Approach, from non-linear control theory, in order to perform the encryption/decryption of the signal to be transmitted. A model/transmitter system is designed, generating a key of chaotic pulses in discrete-time. A plant/receiver system uses the above mentioned key to unlock the mechanism. Two alternative schemes to transmit the private chaotic key are proposed. The first one utilizes two transmission channels. One channel is used to encrypt the chaotic key and the other is used to achieve output synchronization. The second alternative uses only one transmission channel for obtaining synchronization and encryption of the chaotic key. In both cases, the private chaotic key is encrypted again with chaos to solve secure communication-related problems. The results obtained via simulations contribute to enhance the electronic locking devices.     

Policy iteration optimal tracking control for chaotic systems by using an adaptive dynamic programming approach

A policy iteration algorithm of adaptive dynamic programming(ADP) is developed to solve the optimal tracking control for a class of discrete-time chaotic systems. By system transformations, the optimal tracking problem is transformed into an optimal regulation one. The policy iteration algorithm for discrete-time chaotic systems is first described. Then,the convergence and admissibility properties of the developed policy iteration algorithm are presented, which show that the transformed chaotic system can be stabilized under an arbitrary iterative control law and the iterative performance index function simultaneously converges to the optimum. By implementing the policy iteration algorithm via neural networks,the developed optimal tracking control scheme for chaotic systems is verified by a simulation.     

Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional(2D) systems.The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded(polytope type) uncertain domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.     

数字控制单相全桥电压型逆变电路的改进离散迭代模型

针对数字控制单相全桥电压型逆变电路的非线性动力学特性分析,本文建立了一种改进离散迭代模型. 改进离散迭代模型结合了平均模型和传统离散迭代模型的优点, 能够精确分析数字控制延时以及采样保持过程对系统非线性动力学特性的影响, 可以在保证精确度的前提下显著降低离散迭代建模过程的复杂程度.本文以LC滤波器电容电压外环、电感电流内环反馈加给定电压前馈的数字控制系统为例,建立了数字控制单相全桥电压型逆变电路的改进离散迭代模型,采用新模型分析了系统的非线性动力学特性,并准确预测了系统的稳定范围以及失稳现象. 最后,利用SIMULINK仿真模型和物理实验验证了改进离散迭代模型的正确性和有效性. 关键词： 单相全桥逆变电路 离散迭代模型 数字控制 分岔     

Chaotifying a linear time-invariant system by the state feedback controller and sawtooth function

Another algorithm for chaotification of any given linear time-invariant discrete-time systems is presented. The new chaotification algorithm uses the decentralized control and the continuous sawtooth function, which can generate discrete chaos with an arbitrarily desired amplitude bound. Based on the Marotto theorem, we mathematically prove that the controlled system is chaotic in the sense of Li and Yorke. Finally, a simple example is used to illustrate the effectiveness of the proposed theory and method.     

陈氏混沌系统的采样数据反馈控制

提出了基于采样数据反馈控制技术对陈氏混沌系统进行控制的理论.以给定的采样速率对陈氏混沌系统的输出进行采样.利用采样数据去构造离散时间控制算法,以达到将陈氏混沌系统控制到原点的目的.给出了被控制系统渐近稳定的理论证明,并给出了数值试验的结果. 关键词：     

Stochastic modeling of the dynamics of incident-induced lane traffic states for incident-responsive local ramp control

Incident-induced traffic congestion has been recognized as a critical issue to solve in the development of advanced freeway incident management systems. This paper investigates the applicability of a stochastic optimal control approach to real-time incident-responsive local ramp control on freeways. The architecture of the proposed ramp control system embeds two primary functions including (1) real-time estimation of incident-induced lane traffic states and (2) dynamic prediction of ramp-metering rates in response to the changes of incident impacts. To accomplish the above two goals, a discrete-time nonlinear stochastic optimal control model is proposed, followed by the development of a recursive prediction algorithm. Based on the simulation data, the numerical results of model tests indicate that the proposed method permits relieving incident impacts particularly under low-volume and medium-volume conditions, relative to high-volume lane-blocking conditions. Particularly, the incident-induced queue lengths can be improved by 50.1% and 67.9%, compared to the existing ramp control and control-free strategies, respectively.     

离散时间切换广义系统的一致有限时间稳定性

针对一类离散时间切换广义系统, 研究其一致有限时间稳定性问题. 首先, 把广义系统的有限时间稳定性概念推广到离散切换广义系统; 然后, 利用Lyapunov-like函数方法, 给出了离散切换广义系统在任意给定的切换规则下是正则、 因果的, 且有限时间有界和有限时间稳定的充分条件, 同时给出了保证离散切换广义系统一致有限时间稳定的状态反馈控制器的具体设计方法. 仿真算例结果说明了该控制方法的有效性.