基于未知Prandtl-Ishlinskii回滞的一类不确定非线性系统自适应逆控制

针对带有回滞驱动的一类不确定非线性系统,通过把Prandtl-Ishhnskii模型分解为一个离散的Prandtl-Ishlinskii算子和一个小的有界误差项,采用反步递推的设计方法,实现自适应逆控制器的设计.所设计的自适应逆控制器能保证闭环系统全局稳定.仿真结果进一步证明该控制方法的有效性.     

线性滞不确定系统的鲁棒性研究

本文研究了具有一般摄动表达形式的时滞不确定系统，将不确定项分解为“秩１”形式和相乘形式，利用Ｌｙａｐｕｎｏｖ方法和二次镇定的概念，求得了较为完善的充分条件，并例验证。     

带有时滞的区间不确定正系统的约束控制

研究具有时变时滞的连续不确定正系统的约束控制问题.基于线性规划方法,首先设计状态反馈控制器使得相应的闭环系统是正系统且渐近稳定;然后建立在正性约束下有界的鲁棒状态反馈控制器存在的充分条件,同时给出控制器的设计方法;最后利用仿真算例验证所提出方法的有效性.     

区间参数不确定系统优化的可行性分析

针对过程工业系统的特点,以区间参数表示的不确定非线性系统的优化问题转化为一个极大极小型优化命题,并结合遗传算法和常规非线性优化方法对其可行性进行了分析.最后,通过计算示例表明了上述方法的有效性．     

多时滞不确定系统的H_∞反馈控制

研究了具有多个输入时滞的不确定系统H∞控制问题。本文同时考虑了系统的输入时滞和不确定性,基于Lyapunov稳定性理论,采用线性不等式方法得出了系统的H∞反馈控制器。未引入自由权矩阵和模型变换,减少了计算的复杂性。仿真结果证实了方法的有效性。     

不确定多时滞离散切换系统的输出反馈镇定

针对一类具有多重状态时滞和凸多面体不确定性的离散切换系统,研究该系统在任意切换信号下基于状态观测器的输出反馈鲁棒镇定问题.首先通过状态变量的替换将多时滞项转变成不含时滞项,再利用分段Lyapunov函数和线性矩阵不等式方法,导出凸多面体不确定多时滞离散切换系统基于观测器的输出反馈鲁棒镇定的充分条件,并将此条件转化成为一组线性矩阵不等式的可行性问题,同时给出基于状态观测器的输出反馈控制器.仿真结果表明设计方法是可行有效的.     

非线性不确定系统的积分器实用镇定原理*

给定一类带有匹配不确定性的非线性，其自由系统是指数渐近稳定的条件下，其积分器补偿延拓系统可以用一族光滑反馈控制律实用镇定。     

含约束的非线性不确定系统的鲁棒控制

讨论一类含约束的非线性不确定系统的鲁棒控制问题（这里的不确定性并不要求满足匹配条件）。在一定的假设条件下给出了使该类问题可解的充分条件，构造出相应的鲁棒控制器，该控制器避免了利用微分几何方法所得控制器易产生过度控制的缺点。     

具有最小相位的非线性时变不确定系统的鲁棒镇定

讨论了含有时变未知参变数或扰动的非线性不确定系统的鲁棒镇定问题。     

基于区间估计的不确定推理模型BMI之性质分析

一、引言 1986年,Baldwin在支持逻辑程序设计(SLP)·中引人基于区间估计和不确定推模型~[l],但这个模型缺乏良好的理论基础,也未经大量实践检验,文[2]从经过大量实践检验的YCIN的确定因子模     

Optimal interval controller design for uncertain systems

The interval controller design is a hot issue for uncertain systems, whereas how to design an optimal interval controller under the premise of ensuring system stability is a difficult problem that needs further study. This paper mainly aims at the single input single output uncertain system to propose an optimal interval controller based on the Kharitonov theorem and an interval optimization algorithm, which can guarantee the stability and optimization of a closed-loop interval system. According to the Kharitonov theorem, the optimal interval controller design can be transformed into an optimal controller synthesis issue of multiple vertex objects. An interval particle swarm optimization (IPSO) algorithm is then used to optimize the quadratic performance index with interval variables for each vertex object to obtain the solution domains of the controller parameters, and the vertex method is utilized to prevent interval width expansion or divergence in the iteration. Finally, the intersections of the solution domains for all vertex objects are obtained as the optimal interval solution of interval controller parameters. In addition, the stability verification approach of the closed-loop system and the empirical rule to select the interval particle width are given. Simulation results for typical examples demonstrate that the designed interval controller not only performs optimally but also can robustly stabilize the interval system.     

Delay-range-dependent stability for uncertain stochastic systems with interval time-varying delay and nonlinear perturbations

This paper considers the problem of robust stability for a class of uncertain stochastic systems with interval time-varying delay under nonlinear perturbations. A new delay-dependent method for robust stability of the systems is proposed. The innovation of the method includes employment of a tighter integral inequality and construction of an appropriate type of Lyapunov–Krasovskii functional. The restriction used to bound some trace term in the existing methods is also removed. The resulting criterion derived from this method has advantages over previous ones in that it has less conservatism and enlarges the scope of application. The reduction in conservatism of the proposed criterion is attributed to a method to estimate the upper bound on the stochastic differential of the Lyapunov–Krasovskii functional without neglecting any useful terms in the delay-dependent stability analysis. On the basis of the estimation and by utilizing free-weighting matrices, new delay-range-dependent stability criterion is established in terms of linear matrix inequality. Finally, numerical examples are provided to show the effectiveness and reduced conservatism of the proposed method.     

State estimation and decoupling of unknown inputs in uncertain LPV systems using interval observers

This paper proposes a linear parameter varying (LPV) interval observer for state estimation and unknown inputs decoupling in uncertain continuous-time LPV systems. Two different problems are considered and solved: (1) the evaluation of the set of admissible values for the state at each instant of time; and (2) the unknown input observation, i.e. the design of the observer in such a way that some information about the nature of the unknown inputs affecting the system can be obtained. In both cases, analysis and design conditions, which rely on solving linear matrix inequalities (LMIs), are provided. The effectiveness and appeal of the proposed method is demonstrated using an illustrative application to a two-joint planar robotic manipulator.     

Fault tolerant control of uncertain dynamical systems using interval virtual actuators

In this paper, a model reference fault tolerant control strategy based on a reconfiguration of the reference model, with the addition of a virtual actuator block, is presented for uncertain systems affected by disturbances and sensor noise. In particular, this paper (1) extends the reference model approach to the use of interval state observers, by considering an error feedback controller, which uses the estimated bounds for the error between the real state and the reference state, and (2) extends the virtual actuator approach to the use of interval observers, which means that the virtual actuator is added to the control loop to preserve the nonnegativity of the interval estimation errors and the boundedness of the involved signals, in spite of the fault occurrence. In both cases, the conditions to assure the desired operation of the control loop are provided in terms of linear matrix inequalities. An illustrative example is used to show the main characteristics of the proposed approach.     

An interval observer for uncertain continuous‐time linear systems

To design robust interval observers for uncertain continuous‐time linear systems, a new set‐integration approach is proposed to compute trajectory tubes for the estimation error. Because this approach, the order‐preserving condition on the dynamics of the estimation error is no longer required. Therefore, synthesis methods can be used to compute observer gains that reduce the impact of the system uncertainties on the accuracy of the estimated state enclosures. The performance of the proposed approach is showcased through illustrative numerical examples.     

基于改进朴素贝叶斯的区间不确定性数据分类方法

基于Parzen窗的朴素贝叶斯在区间不确定性数据分类中存在计算复杂度高、空间需求大的不足。针对该问题,提出一种改进的区间不确定性数据分类方法IU-PNBC。首先采用Parzen窗估计区间样本的类条件概率密度函数(CCPDF);然后通过代数插值得到类条件概率密度函数的近似函数;最后利用近似代数插值函数计算样本的后验概率, 并用于预测。通过人工生成的仿真数据和UCI标准数据集验证了算法假设的合理性以及插值点数对IU-PNBC算法分类精度的影响。实验结果表明,当插值点数大于15时,IU-PNBC算法的分类精度趋于稳定,且插值点数越多,算法分类精度越高;该算法可以避免原Parzen窗估计对训练样本的依赖, 并有效降低计算复杂度;同时由于该算法具有远低于基于Parzen窗的朴素贝叶斯的运行时间和空间需求, 因此适合解决数据量较大的区间不确定性数据分类问题。     

Delay-segment-dependent robust stability for uncertain discrete stochastic Markovian jumping systems with interval time delay

This article deals with the problem of robust stochastic stability for a class of uncertain discrete stochastic Markovian jumping systems with time-varying interval delay. By constructing a parameter-dependent Lyapunov–Krasovskii functional and checking its difference in two subintervals, respectively, some novel delay-segment-dependent stability criteria for the addressed system are derived. Two simulation examples are given to show effectiveness of the proposed method.     

基于区间数的不确定性数据聚类算法:UD-OPTICS

在不确定性数据聚类算法的研究中,普遍需要假设不确定性数据服从某种分布,继而获得表示不确定性数据的概率密度函数或概率分布函数,然而这种假设很难保证与实际应用系统中的不确定性数据分布一致。现有的基于密度的算法对初始参数敏感,在对密度不均匀的不确定性数据聚类时,无法发现任意密度的类簇。鉴于这些不足,提出基于区间数的不确定性数据对象排序识别聚类结构算法(UD-OPTICS)。该算法利用区间数理论,结合不确定性数据的相关统计信息来更加合理地表示不确定性数据,提出了低计算复杂度的区间核心距离与区间可达距离的概念与计算方法,将其用于度量不确定性数据间的相似度,拓展类簇与对象排序识别聚类结构。该算法可很好地发现任意密度的类簇。实验结果表明,UD-OPTICS算法具有较高的聚类精度和较低的复杂度。     

车-桥系统的振动分析及控制

推导出了由变速行驶车辆与不同边界和路面不平桥梁组成的系统,在安装调质阻尼器(TMD)后的无量纲运动微分方程.作为其特例,研究了匀变速车辆与简谐路面简支桥梁系统,获得了桥梁跨中的无量纲最大挠度随加速度、减速度、初速度、质量比和路面不平度的变化规律,并对系统发生共振时进行TMD控制.数值计算表明:加速度、减速度、初速度和质量比对桥梁的影响均很大;路面不平度对桥梁的影响不可忽略,因为它甚至有可能使桥梁产生共振;TMD可明显减小桥梁的共振振幅.     

多自由度粘弹性非线性随机系统的瞬态响应

研究了高斯白噪声激励下多自由度粘弹性非线性系统的瞬态响应.首先,通过将粘弹性项对系统的作用近似地简化为对原系统阻尼部分以及刚度部分的修正,得到近似的不具粘弹性项的等效非线性随机系统.然后,应用基于广义谐和函数的随机平均法,导出关于幅值瞬态概率密度的平均Fokker-Planck-Kolmogorov方程.该方程的解可通过多重级数式表示,基函数为幅值相关正交函数,系数为时间函数.应用Galerkin方法,关于时间的系数可由一阶线性微分方程组解得,从而得出幅值响应的瞬态概率密度、状态空间概率密度及幅值统计矩的半解析表达式.最后,以耦合的二自由度Duffing-van der Pol振子系统为例,通过与原系统数值模拟结果的比较分析验证了所提出的半解析方法的有效性,并讨论了粘弹性对系统响应的影响.