非线性控制系统的全局输出调节

讨论了非线性控制系统的全局输出调节.首先推广精确线性化方法,通过状态反馈 和微分同胚将非线性系统的全局输出调节问题,转化为线性系统对非线性系统的跟踪问题. 通过提出可解性的概念,得到线性系统对非线性系统全局跟踪的条件,该结果是线性系统结 果的推广.在反馈同胚变换全局成立条件下,得到非线性控制系统全局输出调节问题的充分 条件,该条件对外部系统只做较弱的可解性假设,在反馈同胚变换局部成立的条件下,可得局 部结果.     

非线性控制系统的全局输出调节1)

讨论了非线性控制系统的全局输出调节.首先推广精确线性化方法,通过状态反馈和微分同胚将非线性系统的全局输出调节问题,转化为线性系统对非线性系统的跟踪问题.通过提出可解性的概念,得到线性系统对非线性系统全局跟踪的条件,该结果是线性系统结果的推广.在反馈同胚变换全局成立条件下,得到非线性控制系统全局输出调节问题的充分条件,该条件对外部系统只做较弱的可解性假设,在反馈同胚变换局部成立的条件下,可得局部结果.     

仿射非线性联级系统的全局光滑镇定

研究一般的仿射非线性联级系统的全局光滑可镇定.在其一子系统为光滑反馈无源的条 件下,运用无源性原理和动力学系统的极限集理论,给出了整个联级系统全局镇定的充分条 件,拓展了现有的全局镇定结果.最后给出两个例子予以说明.     

DC-DC变换器在恒功率负载下的能控性

带有恒功率负载的DC-DC变换器是切换非线性系统.以Boost变换器为例,本文建立了其切换系统模型;它包括三个模态.模态I,II,III分别对应于开关器件导通、关断、电感电流断续时的电路拓扑.因为电容电压是非负的,所以本文对平面拓扑学的最新结果加以修正,导出了半平面仿射非线性系统全局能控的充分必要条件——判别函数在任意非零控制曲线上变号.据此证明了模态II的全局能控性.由于模态II为运转中的必经阶段,故切换系统能控.研究方法也适用于Buck等变换器的能控性分析.     

一类非仿射非线性时滞系统的动态状态反馈镇定

本文讨论了一类非仿射非线性时滞系统的全局镇定问题.通过引入辅助积分系统和构造合适的LyapunovKrosovskii泛函,提出了一种基于反推法的时滞无关动态状态反馈控制器,所提控制方法无需时滞的任何先验知识.利用Lyapunov稳定性理论证明了该控制策略能够保证非仿射时滞系统状态渐近收敛于原点,且所有闭环信号全局有界.一个仿真实例进一步验证了所得控制方案的可行性与有效性.     

路面激扰与电磁激扰下电动轮车辆系统非线性全局动态特性研究

为研究电动轮车辆系统在路面 电磁联合激励下的非线性振动特性,并挖掘参数与初始条件协同作用下系统全局动力学信息,建立了计及悬架系统和轮胎的非线性弹簧力和阻尼力的电动轮车辆系统两自由度1/4垂向振动非光滑非线性时变动力学模型,考虑外部激励的谐波性和随机性以及电磁激励的分段周期性,得到了含谐波性、随机性和周期性的复杂外激励模型,分析了驱动电机转速与多初值的关联性对系统动力学共存行为及其分岔的影响规律,研究了共存运动的多样性及其吸引域的拓扑构型,揭示了转速对系统全局动力学稳定性的影响机理.结果表明：电机转速与多初值协同作用诱发系统出现多样性的共存运动,共存运动吸引域的拓扑结构复杂多样,部分共存运动的振动幅值可能较大亦可能很小,其全局动力学稳定性差异较大.电机转速与初值的协同作用对电动轮车辆系统非线性振动和全局动态特性的影响不予忽视.本文研究对电动轮车辆系统的动态性能改善和结构优化具有重要的理论意义和工程价值.     

一类非线性系统全局有限时间观测器设计

本文首先讨论了非线性系统的有限时间稳定, 并给出了其全局有限时间稳定的一个充分条件. 然后, 利用几何齐次理论、Lyapunov稳定性理论, 并通过构造一个增益适应律, 对一类具有下三角结构的非线性系统, 讨论其全局有限时间稳定状态观测器的设计问题, 所设计的观测器是连续非光滑的, 能够在有限时间段内实现状态的精确重构.     

脉冲时滞Hopfield神经网络的全局指数稳定性

研究一类具有脉冲控制的时滞Hopfideld神经网络的全局指数稳定性,通过Lyapunov-Krasovskii稳定性理论和Halanay不等式等方法,构造合适的Lyapunov泛函,利用不等式技巧得到了确保时滞神经网络在脉冲控制下全局指数稳定的一个充分条件,保证了Hofidd神经网络在脉冲控制下的全局指数稳定,并估计了系统的指数收敛率.为了便于计算和验证结论的有效性,给出一个简化的充分条件.最后通过数值实例的实验仿真证实了结论的有效性、可行性.     

一类广义离散Logistic系统的全局吸引性

研究了一类广义离散Logistic系统的全局吸引性,运用差分不等式的技巧得到了该系统正平衡态全局吸引的充分条件,通过数值模拟,验证了结论的可行性。     

离散捕食系统的持久性和全局稳定性

研究一类带有Beddington．DeAngelis功能性反应和时滞的多维离散食饵．捕食系统的持久性和全局稳定性。利用差分方程的比较原理,给出了系统持久性的充分条件;应用估值方法推导得到系统全局稳定性的充分条件;使用不动点理论,证明了系统周期解的存在性和全局稳定性。     

Further results on strict Lyapunov functions for rapidly time-varying nonlinear systems

We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable. This leads to new sufficient conditions for uniform global exponential, uniform global asymptotic, and input-to-state stability of fast time-varying dynamics. We also construct strict Lyapunov functions for our systems using a strictification approach. We illustrate our results using several examples.     

Global search in a noncovex optimal control problem

A nonconvex optimal control problem with the Bolza objective functional is considered. The objective functional is specified by functions represented by the difference of two convex functions (Alexandrov functions). New necessary and sufficient global optimality conditions for minimizing sequences of controls are proved. These conditions provide the basis for a theoretical method for finding global optimal controls; the global convergence of this method is proved.     

A component-wise analysis of constructible match cost functions for global stereopsis

Match cost functions are common elements of every stereopsis algorithm that are used to provide a dissimilarity measure between pixels in different images. Global stereopsis algorithms incorporate assumptions about the smoothness of the resulting distance map that can interact with match cost functions in unpredictable ways. In this paper, we present a large-scale study on the relative performance of a structured set of match cost functions within several global stereopsis frameworks. We compare 272 match cost functions that are built from component parts in the context of four global stereopsis frameworks with a data set consisting of 57 stereo image pairs at three different variances of synthetic sensor noise. From our analysis, we infer a set of general rules that can be used to guide derivation of match cost functions for use in global stereopsis algorithms.     

Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions

This paper investigates the global asymptotic stability of the periodic solution for a general class of neural networks whose neuron activation functions are modeled by discontinuous functions with linear growth property. By using Leray-Schauder alternative theorem, the existence of the periodic solution is proved. Based on the matrix theory and generalized Lyapunov approach, a sufficient condition which ensures the global asymptotical stability of a unique periodic solution is presented. The obtained results can be applied to check the global asymptotical stability of discontinuous neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also conform the validity of Forti’s conjecture for discontinuous neural networks with linear growth activation functions. Two illustrative examples are given to demonstrate the effectiveness of the present results.     

Global exponential stability in Lagrange sense for neutral type recurrent neural networks

In this paper, the global exponential stability in Lagrange sense for continuous neutral type recurrent neural networks (NRNNs) with multiple time delays is studied. Three different types of activation functions are considered, including general bounded and two types of sigmoid activation functions. By constructing appropriate Lyapunov functions, some easily verifiable criteria for the ultimate boundedness and global exponential attractivity of NRNNs are obtained. These results can be applied to monostable and multistable neural networks as well as chaos control and chaos synchronization.     

REMARKS ON THE CONCEPT OF DYNAMICAL SYSTEMS

In this paper, the difference between the concepts of the states of a time system introduced in [1] and of the global state sets of general systems introduced in [3] is discussed. A generalization of the concepts of the global state sets and the global systems-response functions of general systems in given. The constructions of the global state sets and the corresponding global systems-response functions of a system are studied. A list of different definitions of dynamical systems is given, from which a few problems are asked, and a new definition of dynamical systems is given, which is a concept based on the mathematical models of general systems and time systems posed in [2, 3].     

多元多峰值目标函数在MATLAB中的优化

采用MATLAB的遗传算法,利用强大的数学计算能力和遗传工具箱,在全局搜索空间内寻找极值点,能够有效地对多元多峰值函数进行优化,避免了利用传统优化方法在多元多峰值函数优化过程中陷入局部极值点的优化误区。同时简要介绍了遗传算法的特点、流程和优化工具箱,通过实际编程优化,说明基于MATLAB的遗传算法是一种具有良好的全局寻优的优化工具。     

A new filled function applied to global optimization

The filled function method (FFM) is an approach to find the global minimizer of multi-modal functions. The numerical applicability of conventional filled functions is limited as they are defined on either exponential or logarithmic terms. This paper proposes a new filled function that does not have such disadvantages. An algorithm is presented according to the theoretical analysis. A computer program is designed, implemented, and tested. Numerical experiments on typical testing functions show that the new approach is superior to the conventional one. The result of optimization design for an electrical machine is also reported.Scope and purposeIn the context of mathematical programming, global optimization is concerned with the theory and algorithms on minima of multi-modal functions. In general, global optimization approaches can be classified into two categories: probabilistic and deterministic. The former can usually be applied to general multi-modal functions, whereas the latter typically concentrates on some particular classes of functions. The filled function method is one of a few deterministic approaches which intend to find the global minimum for general multi-modal functions. However, the numerical performance of conventional filled functions is undesirable as they are defined on either exponential or logarithmic terms or multiple parameters. This paper proposes a new filled function that does not have the above disadvantages. The present work consists of theoretical analysis, algorithm design, computer implementation, mathematical validation, and engineering application.     

Global optimality of approximate dynamic programming and its use in non-convex function minimization

This study investigates the global optimality of approximate dynamic programming (ADP) based solutions using neural networks for optimal control problems with fixed final time. Issues including whether or not the cost function terms and the system dynamics need to be convex functions with respect to their respective inputs are discussed and sufficient conditions for global optimality of the result are derived. Next, a new idea is presented to use ADP with neural networks for optimization of non-convex smooth functions. It is shown that any initial guess leads to direct movement toward the proximity of the global optimum of the function. This behavior is in contrast with gradient based optimization methods in which the movement is guided by the shape of the local level curves. Illustrative examples are provided with single and multi-variable functions that demonstrate the potential of the proposed method.     

拥塞管理模型在网络对抗中的应用

分析一种在通讯网络中进行拥塞管理的经济模型。这个模型由用户的效用函数和用户对拥塞的延时敏感函数组成,并引入经济学中边际消费的概念来分析网络系统的全局最优性。通过分析表明当用户的效用函数均为线性且用户对延时的敏感系数不等时所得到的全局最优点不是内点,即资源没有达到最优分配,这可由改变效用函数的形式和使用户对延时的敏感系数相等来弥补。数值算例说明了此种分析方法的正确性。