基于拟线性化方法的非线性系统闭环反馈控制保辛算法

提出了一种求解非线性系统闭环反馈控制问题的保辛算法．首先,通过拟线性化方法将非线性系统最优控制问题转化为线性非齐次Hamilton系统两端边值问题的迭代格式求解．然后,通过作用量变分原理与生成函数构造了保辛的数值算法,且该算法保持了原Hamilton系统的辛几何性质．最后,通过时间步的递进完成状态与控制变量的更新,进而达到闭环控制的目的．数值算例表明:保辛算法具有较高的计算精度和较快的收敛速度．此外,将闭环反馈控制与开环控制分别应用于驱动小车上的倒立摆控制系统中,结果表明:在存在初始偏差的情况下,开环控制会导致稳定控制任务的失败,而闭环反馈控制能够在一段时间后消除初始偏差的影响,并使系统达到稳定状态．     

一类流固耦合系统强解的存在性问题

本文主要讨论一类多刚体与粘性系数依赖于密度的不可压缩流体耦合系统的强解存在性问题.首先,利用变量替换建立本文研究对象对应的非线性微分方程,然后,利用Garlerkin逼近方法获得线性化问题的光滑解,从而可以构造出原问题的逼近解.通过估计逼近解的一致有界性,最后证明了一类描述多刚体在不可压缩流体中运动的耦合系统强解的存在...     

一类非仿射非线性系统的神经网络自适应跟踪控制

考虑了一类具有零动态的非仿射非线性不确定系统的神经网络直接自适应跟踪控制问题.控制信号由神经网络系统直接产生,无需另外设计系统估计器及鲁棒控制项.采用梯度下降方法以最小化神经网络控制器与未知理想控制器的误差代价函数产生神经网络白适应参数更新律.应用Lyapunov方法证明了闭环系统的稳定性及跟踪误差和相应闭环系统的所有状态最终一致有界性.最后针对带有外部扰动的非仿射非线性系统的仿真结果验证了该文方法的有效性.     

广义系统渐近稳定性的一种新的Lyapunov判别方法

本文中，对广义系统构造了一种新的Lyapunov函数，并给出相应的渐近稳定性的Laypunov判别方法。另外，我们证明了当广义系数为R－能稳时，必存在一反馈控制使得闭环系统为渐近稳定性的。     

指数分布场合系统应力强度模型可靠度的统计推断

利用最大似然估计和广义区间估计方法,研究了元件的强度和承受的应力均服从指数分布时系统应力强度模型可靠度的估计问题,导出了可靠度的最大似然估计和广义区间估计.同时也讨论了模型的拟合检验问题.利用模拟方法研究了提出的广义置信区间的覆盖率和拟合检验的功效,模拟结果表明提出的广义置信区间的覆盖率与名义置信系数是一致的,提出的拟合检验的功效是好的.最后用一个例子说明提出的方法.     

有限时间迭代学习控制

针对任意初态情形, 借助于初始修正吸引子的概念,讨论不确定时变系统能够达到实际完全跟踪性能的迭代学习控制方法.闭环系统中含有限时间控制作用, 在预先指定的区间上实现零误差跟踪,且起始段的系统输出轨迹也可预先规划.分别讨论部分限幅学习与完全限幅学习, 证明闭环系统中各变量的一致有界性以及误差序列的一致收敛性. 变量有界性证明得益于提出的限幅学习算法,特别是完全限幅学习算法可确保参数估值的变化范围.     

Euler-Bernoulli梁方程基于边界分数阶导数反馈控制的镇定

研究具有边界控制的Euler-Bernoulli梁方程基于边界分数阶导数反馈控制的镇定问题.首先,给出开环系统在Salamon意义下的适定性;其次,运用半群方法和LaSalle不变原理,证明了闭环系统生成C_0-半群并且闭环系统是渐近稳定的;最后,设计了一个未知输入类型的状态观测器,其观测器状态渐近收敛于原系统的状态.     

基于系统动力学视角的生态安全可接受风险研究

与传统概率理论处理生态灾害风险特性不同,是从系统动力学的角度出发,构建生态灾害控制两阶段模型,分别从开环策略与闭环策略阐述了两点:对生态灾害风险事故损失率估计越精确,造成生态灾害的损失额越小;要使生态灾害接近于可接受风险标准并趋于稳定,就必须持续增加资源投入,不断降低生态灾害发生的概率.说明了随着经济体的功能与结构的复杂化,生态灾害可接受风险趋于稳定的情况下,初级控制与次级控制的资金投入量要持续增长.     

离散时间大种群随机多智能体系统的线性二次分散动态博弈

研究具有耦合二次型随机性能指标的离散时间大种群随机多智能体系统的分散博弈问题.系统所受的噪声干扰为条件二阶矩有界的鞅差序列,比以往研究所考虑的高斯白噪声情形更具有广泛性.采用状态聚集方法构造了对种群状态平均的估计,基于Nash必然等价原理设计了分散控制律,并利用概率极限理论分析了闭环系统的稳定性和最优性.主要结果包括(1)证明了对种群状态的平均的估计在某种范数意义下的强一致性,即种群状态的平均与其估计值之间的误差在该范数意义下将随系统个体数N的增加几乎必然收敛于0;(2)证明了闭环系统的几乎必然一致稳定性,即系统的稳定性与种群个体数N无关;(3)证明了所设计的分散控制律是几乎必然渐近Nash均衡策略.     

三边树形一维Euler-Bernoulli梁网络的L2-适定性和正则性

文章考虑了由三根Euler-Bernoulli梁构成的一维网络系统.通过构造适当的乘子,文章证明了开环网络系统是L²-适定的.根据输入-输出传递函数的渐近分析估计,验证了开环系统的正则性.最后,进一步讨论了其他边界条件.     

Lyapunov reducibility and stabilization of nonstationary systems with an observer

For a linear nonstationary control system with an observer, we assume that the coefficients are locally Lebesgue integrable and integrally bounded on ℝ and construct a linear feedback such that the closed-loop plant-controller system is Lyapunov reducible to the special triangular form corresponding to an independent shift of the diagonal coefficients in the original system and in the system of asymptotic estimation of the state by an arbitrary pregiven quantity. For a periodic system, we prove that the constructed controls and Lyapunov transformation are periodic. We obtain corollaries on the uniform stabilization and global controllability of the central and singular exponents of the system.     

Adaptive regulation for deterministic systems

For the linear deterministic system with unknown orders and coefficients adaptive controls are given so that the closed-loop system is stabilized and the unknown parameters are consistently estimated. Moreover, if the parameter estimation is ignored, then the system input and output can be reduced to zero with an exponential rate.This project is supported by the National Natural Science Foundation of China.In Commemoration of the 15th Anniversary of the Acta Mathematicae Applicatae Sinica.     

Computation of alternated reachability tubes for linear control systems under uncertainty

The problem of constructing the reachability domain for linear control system in a presence of geometrically bounded unknown disturbance is considered. A high actuality of the problem for engineering applications requires an efficient calculation technique for the reach sets in a class of closed-loop control. The technique suggested in the article is based on the ellipsoidal approximations developed by A.B. Kurzhansky for the alternated reachability domains. In the article these estimates are complemented with an adaptive regularization to guarantee the continuability of the ellipsoidal estimates. The quadratic structure of the regularization combines well with an ellipsoidal nature of the estimates thus making it possible to adjust the existing ellipsoidal estimation schema in a transparent fashion for achieving the continuable and non-singular estimates via adaptive choice of regularization parameters.     

Simultaneous change point analysis and variable selection in a regression problem

In this paper, an information-based criterion is proposed for carrying out change point analysis and variable selection simultaneously in linear models with a possible change point. Under some weak conditions, this criterion is shown to be strongly consistent in the sense that with probability one, it chooses the smallest true model for large n. Its byproducts include strongly consistent estimates of the regression coefficients regardless if there is a change point. In case that there is a change point, its byproducts also include a strongly consistent estimate of the change point parameter. In addition, an algorithm is given which has significantly reduced the computation time needed by the proposed criterion for the same precision. Results from a simulation study are also presented.     

A note on constrained M-estimation and its recursive analog in multivariate linear regression models

In this paper, the constrained M-estimation of the regression coefficients and scatter parameters in a general multivariate linear regression model is considered. Since the constrained M-estimation is not easy to compute, an up-dating recursion procedure is proposed to simplify the computation of the estimators when a new observation is obtained. We show that, under mild conditions, the recursion estimates are strongly consistent. In addition, the asymptotic normality of the recursive constrained M-estimators of regression coefficients is established. A Monte Carlo simulation study of the recursion estimates is also provided. Besides, robustness and asymptotic behavior of constrained M-estimators are briefly discussed. The research was supported by the Natural Sciences and Engineering Research Council of Canada     

State Estimation and Reliable Control of Singular Markovian Systems with Distributed State Delays and Input Delays

This paper is concerned with state estimation and reliable control for singular Markovian jump systems with distributed state delays and input delays. Firstly, an observer is designed to estimate the system states, and a reliable controller is proposed based on the state estimates. Moreover, some conditions for the mean-square exponential admissibility of the overall closed-loop system are derived in terms of strict linear matrix inequality (LMI).     

Stabilization of nonlinear discrete-time dynamic control systems with a parameter and state-dependent coefficients

A numerical-analytical algorithm for designing nonlinear stabilizing regulators for the class of nonlinear discrete-time control systems is proposed that significantly reduces computational costs. The resulting regulator is suboptimal with respect to the constructed quadratic functional with state-dependent coefficients. The conditions for the stability of the closed-loop system are established, and a stability result is stated. Numerical results are presented showing that the nonlinear regulator designed is superior to the linear one with respect to both nonlinear and standard time-invariant cost functionals. An example demonstrates that the closed-loop system is uniformly asymptotically stable.     

On strongly consistent estimates of regression coefficients when the errors are not independently and identically distributed

In this paper, the author proposes two methods of estimation of the regression coefficients when the errors are not distributed identically and independently and have a nonzero mean. The estimates proved in this paper are shown to be strongly consistent and mean square consistent.     

On the Boundary Control of a Hybrid System with Variable Coefficients

A model of the spacecraft control laboratory experiment with variable coefficients is considered. It is shown that the closed-loop system under boundary feedback damping has a sequence of generalized eigenfunctions, which form a Riesz basis for the state Hilbert space. The spectrum-determined growth condition, the exponential stability, and an asymptotic expression of the spectrum are obtained. Moreover, the exact controllability and exact observability of the system are also presented.     

Linear–quadratic stochastic two-person nonzero-sum differential games: Open-loop and closed-loop Nash equilibria

In this paper, we consider a linear–quadratic stochastic two-person nonzero-sum differential game. Open-loop and closed-loop Nash equilibria are introduced. The existence of the former is characterized by the solvability of a system of forward–backward stochastic differential equations, and that of the latter is characterized by the solvability of a system of coupled symmetric Riccati differential equations. Sometimes, open-loop Nash equilibria admit a closed-loop representation, via the solution to a system of non-symmetric Riccati equations, which could be different from the outcome of the closed-loop Nash equilibria in general. However, it is found that for the case of zero-sum differential games, the Riccati equation system for the closed-loop representation of an open-loop saddle point coincides with that for the closed-loop saddle point, which leads to the conclusion that the closed-loop representation of an open-loop saddle point is the outcome of the corresponding closed-loop saddle point as long as both exist. In particular, for linear–quadratic optimal control problem, the closed-loop representation of an open-loop optimal control coincides with the outcome of the corresponding closed-loop optimal strategy, provided both exist.