基于不确定互补判断矩阵的多目标决策方法研究

针对多目标决策中两种不确定互补判断矩阵形式(区间数互补判断矩阵与三角模糊数互补判断矩阵),给出了各自的模型及其排序方法,并对一些方法进行了推广,提出了一些模型的新方法,为不确定互补判断矩阵排序方法的进一步研究奠定了基础.     

基于包含原理多重叠互联系统动态结构分析

根据系统包含原理和对对分解方法,研究多重叠互联系统当子系统加入和脱离时系统模型结构的动态变化问题.通过将子系统添加矩阵与删除矩阵的有机结合,构建基于子系统数量变化的行和列组动态结构变化矩阵,使待加入和脱离的子系统与原系统相关子系统之间的信息结构动态的连接和断开.最后,将其应用于多区域互联电力系统AGC中,并采用多重叠分散LQ控制.仿真结果表明了结构变化后系统的稳定情况.     

切换系统的自适应广义预测控制

针对一类切换系统研究了含有输出预测误差的自适应广义预测控制问题．切换律由有限个子系统的输出预测误差确定．对于单个子系统和多个子系统两种情况,证明了所提出的广义预测控制直接算法能够保证系统的全局收敛性．该算法克服了传统自适应控制固有的收敛速度慢且暂态误差较大的缺点．     

广义不确定下广义多目标博弈弱Pareto-Nash均衡点集的存在性与本质连通区

引入具有不确定参数的n人广义多目标博弈,这里局中人了解不确定性参数的变化区域,而且个人的参数变化与其他局中人的行为密切相关.我们定义广义不确定下广义多目标博弈的弱Pareto-Nash均衡.进一步我们证明广义不确定下广义多目标博弈的弱Pare-Nash均衡点集的存在性与本质连通区的存在性.     

基于极大极小方法的一类非线性系统的自适应控制

研究一类具有非线性不确定参数的非线性系统的自适应模型参考跟踪问题.假设系统的非线性项关于不确定参数是凸或凹的.去掉了在先前有关研究中要求参考模型矩阵有小于零的实特征值的条件.既考虑了状态反馈控制方式,也考虑了输出反馈控制方式.在采用输出反馈控制时,假设非线性项满足李普希兹条件,但李普希兹常数未知.基于一种极大极小方法,提出了一种自适应控制器的设计方法.控制器是连续的,能保证闭环系统的所有变量有界,并且渐近精确跟踪参考模型.举例说明了本结论的有用性.     

不确定语言多属性决策的组合方法

研究了属性权重完全未知、属性值以不确定语言变量形式给出的不确定语言多属性决策问题.首先引入了不确定语言变量的运算法则,以及不确定语言变量之间比较的可能度公式,给出了不确定语言变量间的距离的概念.针对属性权重完全未知的情形,给出了一个求解权重的组合公式.然后利用不确定语言加权平均(ULWA)算子,对不确定语言决策信息进行加权集成,并利用可能度公式构造可能度矩阵(互补判断矩阵),继而利用互补判断矩阵排序公式对决策方案进行排序和择优.最后进行了实例分析.     

一种基于三参数区间灰色语言变量的多属性群决策方法

针对属性值为三参数区间灰色语言变量的不确定型多属性决策问题进行了研究,本文将语言变量和三参数区间数融合, 提出了三参数区间灰色语言变量的概念, 定义了三参数区间灰色语言变量的运算规则和可能度公式,在此基础上建立了基于投影模型的三参数区间灰色语言变量的多属性群决策方法。最后,通过对移动银行服务质量评估案例验证本模型的有效性。     

具有非线性扰动的不确定多个变时滞系统的有记忆非脆弱状态反馈控制（英文）

本文研究不确定非线性多时滞系统的非脆弱鲁棒镇定问题.状态和输入矩阵中的参数不确定性假设是范数有界.延迟是未知的,但随时间变化范围是已知的.对所有容许的参数不确定性,非脆弱鲁棒镇定问题是设计一个记忆脆弱的状态反馈控制器使得闭环系统是鲁棒稳定.利用Lyapunov泛函和自由权矩阵方法,以线性矩阵不等式(LMI)的的形式,得到时滞依赖充分镇定判据.数值例子说明所提出的理论结果的有效性.     

求解线性系统的广义二阶段多分裂迭代法的收敛性

一般二阶段多分裂迭代法的权矩阵都是预先给出的,在迭代过程中并不知道它的优劣.提出了广义的二阶段多分裂迭代法,它的加权矩阵不必预先给出,而是在迭代过程中通过求超平面上的最优解而得出的随迭代步数变化的动态的权矩阵.这样,动态的权矩阵能使得第k步的近似解更加逼近问题的真解.文中建立了新方法的收敛性理论,并以数值实验验证新方法的有效性.     

参数不确定性广义周期时变系统的鲁棒H_∞控制

研究状态矩阵和控制输入矩阵均具不确定性广义周期时变系统的鲁棒H_∞控制问题.提出参数不确定性广义周期时变系统广义可镇定和广义二次可镇定且具有H_∞性能指标的概念,利用线性矩阵不等式(LMI)方法,得到了参数不确定性广义周期时变系统广义二次可镇定且具有H_∞性能指标γ的充要条件,给出了相应的鲁棒H_∞状态反馈控制律的设计方法.最后,通过数值算例说明了设计方法的有效性.     

Adaptive output feedback asymptotic stabilization of nonholonomic systems with uncertainties

A global adaptive output feedback control strategy is presented for a class of nonholonomic systems in generalized chained form with drift nonlinearity and unknown virtual control parameters. The purpose is to design a nonlinear output feedback switching controller such that the closed-loop system is globally asymptotically stable. By using the input-state scaling technique and an integrator back-stepping approach, an output feedback controller is given. A filter of observer gain is introduced for state and parameter estimates. Meanwhile, in order to avoid the over-parameters, a tuning function technique is utilized. A novel switching control strategy based on the output measurement of the first subsystem rather than time is used to overcome the uncontrollability of the x₀-subsystem in the origin. The proposed controller can guarantee that all the system states globally converge to the origin, while other signals maintain bounded. The numerical simulation testifies the effectiveness.     

一类不确定广义周期时变系统的鲁棒H_∞控制

本文研究了状态矩阵具不确定性广义周期时变系统的鲁棒H∞控制问题.利用线性矩阵不等式(LMI)方法,在给出不确定广义周期时变系统广义可镇定和广义二次可镇定且具有H∞性能指标概念的基础上,得到了该系统广义二次可镇定且具有H∞性能指标γ的充要条件,并给出了相应的鲁棒H∞状态反馈控制律的设计方法,推广了周期系统的鲁棒控制理论结果.最后,通过数值算例说明了设计方法的有效性.     

Correlation propagation for uncertainty analysis of structures based on a non-probabilistic ellipsoidal model

Traditional non-probabilistic methods for uncertainty propagation problems evaluate only the lower and upper bounds of structural responses, lacking any analysis of the correlations among the structural multi-responses. In this paper, a new non-probabilistic correlation propagation method is proposed to effectively evaluate the intervals and non-probabilistic correlation matrix of the structural responses. The uncertainty propagation process with correlated parameters is first decomposed into an interval propagation problem and a correlation propagation problem. The ellipsoidal model is then utilized to describe the uncertainty domain of the correlated parameters. For the interval propagation problem, a subinterval decomposition analysis method is developed based on the ellipsoidal model to efficiently evaluate the intervals of responses with a low computational cost. More importantly, the non-probabilistic correlation propagation equations are newly derived for theoretically predicting the correlations among the uncertain responses. Finally, the multi-dimensional ellipsoidal model is adopted again to represent both uncertainties and correlations of multi-responses. Three examples are presented to examine the accuracy and effectiveness of the proposed method both numerically and experimentally.     

Uncertainty propagation in stochastic fractional order processes using spectral methods: A hybrid approach

Stochastic spectral methods are widely used in uncertainty propagation thanks to its ability to obtain highly accurate solution with less computational demand. A novel hybrid spectral method is proposed here that combines generalized polynomial chaos (gPC) and operational matrix approaches. The hybrid method takes advantage of gPC’s efficient handling of large parameter uncertainties and overcomes its limited applicability to systems with relatively highly correlated inputs. The hybrid method’s use of operational matrices allows analyses of systems with low input correlations without suffering its restriction to small parameter uncertainties. The hybrid method is aimed to propagate uncertainties in fractional order systems with random parameters and random inputs with low correlation lengths. It is validated through several examples with different stochastic uncertainties. Comparison with Monte Carlo and gPC demonstrates the superior computational efficiency of the proposed method.     

Decentralized Reliable Control of Interconnected Time-Delay Systems Against Sensor Failures

In this paper, we study the problem of designing decentralized reliable feedback control methods under a class of control failures for a class of linear interconnected continuous-time systems having internal subsystem time-delays and additional time-delay couplings. These failures are described by a model that takes into consideration possible outages or partial failures in every single actuator of each decentralized controller. The decentralized control design is performed through two steps. First, a decentralized stabilizing reliable feedback control set is derived at the subsystem level through the construction of appropriate Lyapunov-Krasovskii functional and, second, a feasible linear matrix inequalities procedure is then established for the effective construction of the control set under different feedback schemes. Two schemes are considered: the first is based on state-measurement and the second utilizes static output-feedback. The decentralized feedback gains in both schemes are determined by convex optimization over linear matrix inequalities. We characterize decentralized linear matrix inequality-based feasibility conditions such that every local closed-loop subsystem of the linear interconnected delay system is delay-dependent robustly asymptotically stable with an γ-level ℒ₂-gain. The developed results are tested on a representative example.     

Three-stage recursive least squares parameter estimation for controlled autoregressive autoregressive systems

A three-stage recursive least squares parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) systems. The basic idea is to decompose a CARAR system into three subsystems, one of which contains one parameter vector, and to identify the parameters of each subsystem one by one. Compared with the recursive generalized least squares algorithm, the dimensions of the involved covariance matrices in each subsystem become small and thus the proposed algorithm has a high computational efficiency. Finally, we verify the proposed algorithm with a simulation example.     

多时滞非线性中立型反馈系统的鲁棒稳定性

The stabilization of a class of neutral systems with multiple time-delays is considered. To stabilize the neutral system with nonlinear uncertainty, a state feedback control law via compound memory and memoryless feedback is derived. by constructed Lyapunov functional, delay-independent stability criteria are proposed that are sufficient to ensure a uniform asymptotic stability property. Finally, two concise examples are provided to illustrate the feasibility of our results.     

Attitude control of rigid spacecraft with disturbance generated by time varying exosystems

This paper is concerned with the problem of attitude control and disturbance rejection of rigid spacecraft in the presence of parameter uncertainty. It is assumed that the external disturbance is generated by some time varying exosystems. The unit quaternion is used as the kinematic variables since it is free of singularity. An internal model and an adaptive control law are proposed. The parameter uncertainty caused by the unknown inertia matrix is handled by combining the semi-tensor product and adaptive control method. The asymptotical stability of the closed-loop system is given via backstepping and Lyapunov analysis. Finally, an illustrative example is provided to show the effectiveness of the proposed approach.     

Decentralized Reliable Control of Interconnected Systems with Time-Varying Delays

In this paper, we study the problem of designing decentralized reliable feedback control methods under a class of control failures for a class of linear interconnected continuous-time systems having internal subsystem time-delays and additional time-delay couplings. These failures are described by a model that takes into consideration possible outages or partial failures in every single actuator of each decentralized controller. The decentralized control design is performed through two steps. First, a decentralized stabilizing reliable feedback control set is derived at the subsystem level through the construction of appropriate Lyapunov-Krasovskii functional and, second, a feasible linear matrix inequalities procedure is then established for the effective construction of the control set under different feedback schemes. Two schemes are considered: the first is based on state measurement and the second utilizes static output feedback. The decentralized feedback gains in both schemes are determined by convex optimization over LMIs. We characterize decentralized linear matrix inequalities (LMIs)-based feasibility conditions such that every local closed-loop subsystem of the linear interconnected delay system is delay-dependent robustly asymptotically stable with a γ-level ℒ₂-gain. The developed results are tested on a representative example.