On existence and uniqueness of solutions to uncertain backward stochastic differential equations简

This paper is concerned with a class of uncertain backward stochastic differential equations （UBSDEs） driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in mod- elling hybrid systems, where the phenomena are simultaneously subjected to two kinds of un- certainties： randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coeffi- cients are proved.     

Input torque sensitivity to uncertain parameters in biped robot

Input torque is the main power to maintain bipedal walking of robot, and can be calculated from trajectory planning and dynamic modeling on biped robot. During bipedal walking, the input torque is usually required to be adjusted due to some uncertain parameters arising from objective or subjective factors in the dynamical model to maintain the pre-planned stable trajectory. Here, a planar 5-link biped robot is used as an illustrating example to investigate the effects of uncertain parameters on the input torques. Kine-matic equations of the biped robot are firstly established by the third-order spline curves based on the trajectory planning method, and the dynamic modeling is accomplished by taking both the certain and uncertain parameters into account. Next, several evaluation indices on input torques are intro-duced to perform sensitivity analysis of the input torque with respect to the uncertain parameters. Finally, based on the Monte Carlo simulation, the values of evaluation indices on input torques are presented, from which all the robot param-eters are classified into three categories, i.e., strongly sensi-tive, sensitive and almost insensitive parameters.     

Global Exponential Stability in Lagrange Sense for Delayed Memristive Neural Networks with Parameter Uncertainties

This paper addresses the Lagrange stability of memristive neural networks with leakage delay and time-varying transmission delays as well as parameter uncertainties. Based on the theory of Filippov''s solution, by using Lyapunov-Krasovskii functionals and the free-weighting matrix method, sufficient conditions in terms of linear matrix inequality (LMI) are given to ascertain the networks with different kinds of activation functions to be stable in Lagrange sense. Meanwhile the estimation of globally attractive sets are given. Finally, numerical simulations are carried out to illustrate the effectiveness of theoretical results.     

Dual characterizations of set containments involving uncertain polyhedral sets in Banach spaces with applications

In this paper, we first give a dual characterization for set containments defined by lower semi-continuous and sublinear functions on Banach spaces. Next, we provide dual characterizations for robust polyhedral containments where a robust counterpart of an uncertain polyhedral set is contained in another polyhedral set or a polyhedral set is contained in a robust counterpart of an uncertain polyhedral set. Finally, as an application, we derive Lagrange multiplier characterizations for robust solutions of the robust uncertain linear programming problems.     

Parameterized OWA operator weights: An extreme point approach

Since Yager first presented the ordered weighted averaging (OWA) operator to aggregate multiple input arguments, it has received much attention from the fields of decision science and computer science. A critical issue when selecting an OWA operator is the determination of the associated weights. For this reason, numerous weight generating methods, including rogramming-based approaches, have appeared in the literature. In this paper, we develop a general method for obtaining OWA operator weights via an extreme point approach. The extreme points are represented by the intersection of an attitudinal character constraint and a fundamental ordered weight simplex. The extreme points are completely identified using the proposed formula, and the OWA operator weights can then be expressed by a convex combination of the identified extreme points. With those identified extreme points, some new OWA operator weights can be generated by a centroid or a user-directed method, which reflects the decision-maker’s incomplete preferences. This line of reasoning is further extended to encompass situations in which the attitudinal character is specified in the form of interval with an aim to relieve the burden of specifying the precise attitudinal character, thus obtaining less-specific expressions that render human judgments readily available. All extreme points corresponding to the uncertain attitudinal character are also obtained by a proposed formula and then used to prioritize the multitude of alternatives. Meanwhile, two dominance rules are effectively used for prioritization of alternatives.     

基于不确定油液光谱数据的综合传动装置剩余寿命预测

原子发射光谱分析得到的磨损微粒元素浓度是综合传动装置性能劣化评估和剩余寿命预测的重要监测指标。由于系统随机劣化过程和光谱测量误差的影响,油液光谱数据中不可避免包含系统劣化随机性和光谱测量不确定性。然而,现有基于油液光谱数据的剩余寿命预测研究中,没有考虑劣化过程的随机性和测量的不确定性对剩余寿命预测的影响。因此,针对综合传动装置劣化随机性和油液光谱数据测量不确定性对寿命预测的影响,提出一种考虑系统随机劣化和数据不确定测量的综合传动装置劣化过程建模方法。基于随机过程首中时间的概念,定义了综合传动装置的剩余寿命;基于Wiener随机过程,建立了考虑系统随机劣化和不确定测量数据的综合传动装置劣化模型,利用极大似然估计方法,估计了劣化过程模型的参数;利用卡尔曼滤波技术,实现了综合传动装置劣化状态的实时估计与更新,进一步得到了考虑系统劣化随机性和光谱数据测量不确定性的剩余寿命分布。研究结果表明,提出的劣化建模方法能够准确估计装置的运行状态,避免了采用条件维护时间对装置进行维护与保养的局限性;综合传动装置的维护时间预测值比条件维护时间延长了193 Mh（113.5%）;考虑光谱数据测量不确定性的剩余寿命预测方法优于不考虑测量不确定性的方法。     

Robust μ -stability for uncertain stochastic neural networks with unbounded time-varying delays

In this paper, we investigate the global robust stability for uncertain stochastic neural networks with unbounded time-varying delays and norm-bounded parameter uncertainties. A new concept of global robust μ-stability in the mean square for neural networks is given first, then by means of the linear matrix inequality (LMI) approach, stability criteria are presented. Several corollaries are also derived. A simple example is presented to demonstrate the effectiveness of the main result.     

经典不确定关系到量子不确定关系的推广及对世界稳定性的应用

一般地引入了经典统计力学的联合概率密度分布,并把其密度函数一般地推广为一般的复函数和它的复共厄的乘积,进而自然地把经典统计力学平均值推广到量子力学的平均值,首次依据联合概率密度分布把经典统计力学的不确定关系严格地推广到量子力学的不确定关系,给出了经典统计力学与量子力学中不确定关系的对应关系,发现了人们对经典统计力学与量子力学不确定关系推导时所各遗漏的一个重要的条件,对不确定关系与此相关的所有的相关文章和书都需修正.最后一般地阐明了世界的稳定性与不确定关系的联系,同时一般地给出了不确定关系失效的条件.     

一类离散不确定线性时滞系统的鲁棒镇定

研究具有时变不确定参数的离散线性时滞系统的鲁棒控制问题,其中不确定性满足匹配条件,利用Ｌｙａｐｕｎｏｖ确定性理论,提出了鲁棒稳定性控制器一种新的设计方法,得到了这类离散不确定线性时滞系统可鲁棒镇定的充分条件。     

On delay-dependent robust exponential stability of stochastic neural networks with mixed time delays and Markovian switching

This paper deals with the global exponential stability analysis problem for a general class of uncertain stochastic neural networks with mixed time delays and Markovian switching. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed stochastic neural network is robustly exponentially stable in the mean square in the presence of parameters uncertainties, mixed time delays, and Markovian switching. By employing new Lyapunov–Krasovskii functionals and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria for the robust exponential stability, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. The criteria derived are dependent on both the discrete time delay and distributed time delay, and, are therefore, less conservative. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria. This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the National Natural Science Foundation of China under Grant 60774073, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the Natural Science Foundation of Jiangsu Education Committee of China under Grant 06KJD110206, the Scientific Innovation Fund of Yangzhou University of China under Grant 2006CXJ002, and the Alexander von Humboldt Foundation of Germany.