一类非线性欠驱动系统的混沌优化LQ控制

提出了一种基于混沌优化线性二次最优控制器权矩阵参数的三级倒立摆控制方法;根据系统控制的目标,设计了一类适合多变量系统的优化性能指标函数;这类性能指标函数综合考虑三级倒立摆系统各个输出间的重要程度,以及动态特性和稳定性要求,结合文中的性能指标函数,首先利用混沌粗搜索得到控制器权矩阵参数的次优解,再在次优解的邻域内继续寻优,得到全局最优的权矩阵参数;利用这种方法得到的LQ控制器,有效地实现了对三级倒立摆的稳定控制。     

多自由度参数振动混沌控制方法研究

基于耦合倒立双摆模型,本文采用Liapunov-Floquet变换,将周期时变系统转化为时不变系统,并引入反馈和极点配置,对该多自由度系统做参数振动进行主动控制.对研究的系统结合单位脉冲响应进行了稳定性分析,并成功地应用于系统混沌控制.     

Impulsive stabilization of high-order hopfield-type neural networks with time-varying delays

This paper studies the problems of global exponential stability for impulsive high-order Hopfield-type neural networks (NNs) with time-varying delays. By employing the Lyapunov-Razumikhin technique, some criteria ensuring global exponential stability are derived. Our results are then used to obtain some sufficient conditions under which some NNs can be forced to converge by impulsive control. Numerical examples are also discussed to illustrate our results.     

Mathematical models for the control of a pest population by infected pest

In this paper, we propose two mathematical models concerning continuous and impulsive pest control strategies, respectively. Therefore, our models are the ordinary differential equations and the impulsive differential equations. As a result, the global asymptotic stability of the equilibria of the ordinary differential equations is studied. In the case when an impulsive control is used, it is observed that there exists a globally asymptotically stable susceptible pest-eradication periodic solution when the amount of infective pests released periodically is larger than some critical value. When the amount of infective pests released is less than this critical value, the system is shown to be permanent, which implies that the trivial susceptible pest-eradication solution loses its stability. Finally, by means of numerical simulation, we obtain the critical values of the control variable under different methods of release of infected pests.     

Global stabilization of the unstable Reaction-Wheel Pendulum

The paper deals with the problem of the Reaction Wheel Pendulum stabilization about unstable (inverted) position for arbitrary initial conditions. Considered mechanical system consists of a physical pendulum with a symmetric disk attached to the end of the pendulum, which is free to spin about an axis parallel to the axis of rotation of the pendulum. The disk is actuated by a DC-motor. The coupling torque generated by the angular acceleration of the disk is used to control of the pendulum. The switching control law is proposed to swinging up the pendulum and balancing it about the inverted position. The nonlinear swinging up control law is proposed ensuring global stabilization of the pendulum about inverted position. The Energy-based Speed-gradient (EBSG) control scheme is used to designing the swinging-up controller. The modification of the EBSG method is proposed to ensure attainability of the inverted position of the pendulum for all initial states of the system. The balance controller is designed on the basis of the Variable Structure Control with forced sliding mode. Numerical simulation results are presented showing achievement of the posed control goal by means of the control action of small magnitude.     

船舶混沌运动的周期脉冲参数微扰控制

针对海上航行船舶非线性运动中存在的混沌现象,为实现对航行船舶的高精度航向控制,本文将脉冲参数微扰方法与横截同宿点理论相结合,提出了一种基于Melnikov方法的简捷船舶混沌运动周期脉冲参数微扰控制方法.该控制方法利用Melnikov函数确定控制脉冲参量关系及取值范围,基于该方法设计的控制器克服了脉冲参量取值难以确定的不足.仿真结果表明,本文所提方法能将混沌系统快速稳定到不同的周期轨道,具有较好的控制效果.     

Continuous and impulsive harvesting strategies in a stage-structured predator–prey model with time delay

In this paper, the continuous and impulsive harvesting policies are considered in a predator–prey system with stage-structure. In the case in which a continuous harvesting is used, it is shown that the mature predator becomes extinct under appropriate conditions. In the case in which an impulsive harvesting is used, using the discrete dynamical system determined by the stroboscopic map, we obtain the mature predator-eradication periodic solution of the system which is globally attractive. The conditions of permanence are established by the method of comparison involving multiple Liapunov functions and auxiliary function. These results indicate that: a short period of pulse harvest is a sufficient condition for the eradication of the population; the impulsive harvest policy is more effective than the continuous one from eradicating predator point of view. Our results offer a more economical and safe strategy in controlling pest in contrast with biological control and chemical control. Furthermore, we give a summary of the dynamic behavior when the impulsive period takes values in different intervals. Finally, numerical results show that the impulsive system we considered has more complex dynamics including quasi-periodic oscillation and chaos.     

周期时变系统的鲁棒自适应重复控制

针对周期时变系统,提出一种鲁棒自适应重复控制方法.该方法利用周期学习律估计周期时变参数,并结合鲁棒自适应方法处理非周期不确定性.与现有重复控制不同的是,在控制器设计中引入了新变量—周期数,利用周期系统的重复特性,使界的逼近误差随周期数的增加而逐渐减少,保证了系统的全局渐近稳定性.同时将该方法应用于一类非线性参数化系统,使系统在非参数化扰动的情形下,输出误差仍能收敛于0,倒立摆模型的仿真验证了此结果.该设计方法适用于消除神经网络逼近误差对重复控制系统的影响,理论证明了基于神经网络的鲁棒自适应重复控制系统中所有变量的有界性和输出误差的渐近收敛性,关于机械臂模型的仿真结果验证了受控系统具有良好的跟踪性能.     

基于混沌搜索的二级倒立摆模糊控制器设计

利用混沌优化的模糊控制方法对二级倒立摆系统进行闭环控制。用混沌算法优化控制器的参数,首先将混沌变量引入到模糊控制器的参数域,并进行全局范围内直接寻优,当获得全局近似最优解后,再缩小寻优区间,根据性能指标,在次优解附近继续寻优,得到全局最优参数。控制结果说明该方法是有效可行的。     

二级倒立摆在受控情况下的运动稳态分析

通过对二级倒立摆系统物理结构的分析,总结了二级倒立摆系统在受控稳定状态下可能出现的各种运动状态。在由单电机控制的二级倒立摆稳定的基础上,分析控制倒立摆系统稳定的控制量与系统稳定运动状态之间存在的关系。通过实验,得到了两级摆杆之间的3种在受控稳定下的具体运动状态,证明了二级倒立摆的运动状态与系统控制中的某些参数存在着明显的关联,并且为从理论上分析这些运动状态和控制参数之间的关系提供了一定的依据。     

Dynamics and Chaos: The Spherical Pendulum

All but the simplest of dynamical systems contain nonlinearities that play an important role in modeling and simulating physical systems. They create unpredictable (chaotic) behavior that is often hidden or neglected in traditional solutions. A simple dynamical system, the spherical pendulum, is introduced to illustrate issues, principles, and effects of chaos in dynamics. The spherical pendulum is a two degrees of freedom nonlinear system with a pivot point in space. The equations of motion for the pendulum are derived, simulated, and animated. A periodical perturbation is applied to the pivot point producing radically different behavior.     

Less conservative conditions for asymptotic stability of impulsive control systems

This note studies the stability of impulsive control systems. A new comparison theorem for asymptotic stability of impulsive differential system is presented. Based on the new result, we derive some less conservative conditions for asymptotic stability of impulsive control systems with impulses at fixed times and the results are used to design impulsive control for a class of nonlinear systems. The class of nonlinear systems considered is also enlarged.     

一级倒立摆状态反馈控制系统设计

倒立摆控制系统是一个复杂的、不稳定的、非线性系统,对倒立摆系统的研究能有效的反映控制中的许多典型问题。对一级直线型倒立摆,首先运用牛顿运动定律建立倒立摆系统的运动方程,进而求出系统的状态空间表达式,建立数学模型。其次运用状态反馈极点配置法,以小车的位移、速度,摆杆与竖直向上的偏角、摆角变化速度作为四个状态变量,由给定的控制要求求出状态反馈增益矩阵,将极点配置在控制要求的位置。另外考虑到系统的某些状态如小车速度和摆杆角速度不容易直接测量等,本文分别基于小车和摆杆子系统设计了两个全维观测器,分别对状态量进行了重构并给出了仿真结果分析。     

强噪声下利用混沌系统测量频率的新方法

在分析混沌形成的基础上,将变结构滑模方法引入到混沌理论中,通过它将处于混沌态的系统控制到稳定周期状态,然后,再用频谱方法测出待检信号的频率。所提出方法的新颖性在于去掉了以往混沌系统测量信号所需的策动力,而将待检信号作为策动力。经实验仿真发现:此方法与以往方法比较具有较高的分辨力。     

Leaderless and leader‐following fixed‐time consensus for multiagent systems via impulsive control

This article addresses the leaderless fixed‐time consensus (LLFTC) and leader‐following fixed‐time consensus (LFFTC) problems for multiagent systems (MASs) via impulsive control. First, a novel fixed‐time stability for impulsive dynamical system is developed. Then the novel fixed‐time impulsive control protocols are designed to achieve leaderless and leader‐following consensus for MASs. Based on the impulsive control theory, fixed‐time stability theory and algebraic graph theory, some sufficient conditions are derived for each agent to achieve LLFTC and LFFTC under the proposed control protocols. Finally, numerical simulations are put forward to validate the theoretical results.     

Mathematical modeling of endocrine regulation subject to circadian rhythm

The 2017 Nobel Prize in Physiology or Medicine awarded for discoveries of molecular mechanisms controlling the circadian rhythm has called attention to the challenging area of nonlinear dynamics that deals with synchronization and entrainment of oscillations. Biological circadian clocks keep time in living organisms, orchestrating hormonal cycles and other periodic rhythms. The periodic oscillations of circadian pacemakers are self-sustained; at the same time, they are entrainable by external periodic signals that adjust characteristics of autonomous oscillations. Whereas modeling of biological oscillators is a well-established research topic, mathematical analysis of entrainment, i.e. the nonlinear phenomena imposed by periodic exogenous signals, remains an open problem. Along with sustained periodic rhythms, periodically forced oscillators can exhibit various “irregular” behaviors, such as quasiperiodic or chaotic trajectories.This paper presents an overview of the mathematical models of circadian rhythm with respect to endocrine regulation, as well as biological background. Dynamics of the human endocrine system, comprising numerous glands and hormones operating under neural control, are highly complex. Therefore, only endocrine subsystems (or axes) supporting certain biological functions are usually studied. Low-order dynamical models that capture the essential characteristics and interactions between a few hormones can than be derived. Goodwin’s oscillator often serves as such a model and is widely regarded as a prototypical biological oscillator. A comparative analysis of forced dynamics arising in two versions of Goodwin’s oscillator is provided in the present paper: the classical continuous oscillator and a more recent impulsive one, capturing e.g. pulsatile secretion of hormones due to neural regulation. The main finding of this study is that, while the continuous oscillator is always forced to a periodic solution by a sufficiently large exogenous signal amplitude, the impulsive one commonly exhibits a quasiperiodic or chaotic behavior due to non-smooth dynamics in entrainment.     

Bifurcations of the horizontally forced spherical pendulum

Various planar motions of the horizontally forced damped spherical pendulum are considered and, in particular, their stability to non-planar perturbations. By making a careful choice of coordinates, all solutions of the planar pendulum can be considered including small amplitude periodic solutions, running oscillations and chaotic solutions. The full nonlinear equations in the chosen coordinates are derived and the symmetries of the system are described. Bifurcation diagrams for various types of solutions are presented. Stability of the chaotic solutions is determined by considering a normal Lyapunov exponent.     

Method of stochastic sensitivity synthesis in a stabilisation problem for nonlinear discrete systems with incomplete information

A problem of the synthesis of the assigned probabilistic distribution near the equilibrium of stochastic nonlinear discrete-time system with incomplete state information is considered. We construct a static feedback regulator which provides a required stochastic sensitivity of this equilibrium. It is shown that this problem is reduced to the solution of some quadratic matrix equations. The solvability of these quadratic equations is analysed, and attainability sets are described. In the two-dimensional case, two variants of the control input are discussed and compared. These general results are applied to the suppression of large-amplitude oscillations around the equilibria of the stochastically forced Henon model with noisy observations. We show how suggested control technique, by minimising the stochastic sensitivity, allows us to suppress chaos and provide a structural stabilisation.     

一种带时间窗口的双脉冲控制器下的忆阻振荡系统滞同步

在真实的环境中实现复杂忆阻振荡系统的同步时, 因为信息干扰及通信问题, 驱动和响应系统之间总是存在信息传输时滞, 即时滞问题具有普遍性; 另外, 脉冲控制信号的输入总是存在输入误差, 并不能实现精确地输入.本文考虑到上述实际存在的信息传输时滞和脉冲输入误差, 设计了一种比较接近真实情况的、灵活的可以带有不同时间窗口和不同控制增益的双脉冲切换控制器, 并且利用该控制器实现了两个复杂忆阻振荡系统的滞同步.基于Lyapunov稳定性理论、矩阵不等式以及脉冲控制等相关理论, 本文找出了实现一类五阶复杂忆阻振荡系统同步的条件.最后的仿真实验进一步验证了本控制方法的可行性.     

带有时变计算时延的倒立摆视觉实时控制研究

针对倒立摆视觉实时控制系统中,通过每帧图像处理检测小车位移和摆杆偏角带来的时变图像处理计算时间,直接影响控制系统采样周期和系统性能的问题,不同于目前不考虑图像处理计算时间或将其视为定时滞进行倒立摆视觉实时控制的研究方法,本文首先构建了倒立摆视觉伺服控制实验平台,考虑倒立摆的小车与摆杆特征,提出了小车位移和摆杆偏角的实时计算方法;然后统计分析了图像处理计算时间的特性并设计了视觉传感事件触发采样策略,进一步刻画了时变时延与计算时间的直接关系,进而建立了带有时变计算时延的倒立摆视觉控制系统闭环模型,证明了系统稳定性并建立了反映图像处理计算时间与系统稳定性之间的关系.最后,仿真和实时控制实验验证了所提方法的可行性和有效性.