On the stability of uncertain polynomials with dependentcoefficients

A sufficient condition is given for reducing the conservatism of the stability bounds for a family of polynomials with dependent coefficients, including nonlinear coefficients. It is also proved that if a finite family of stable polynomials has the same even part, then the polynomial with the even part and the odd part formed by adding any positive multiple of the even parts and odd parts, respectively, of the given family is also stable. Similar results holds if the given family of polynomials has the same odd part. A numerical example with nonlinear coefficients is given to illustrate the technique, and it is observed that the stability bounds obtained are larger than those acquired by Kharitonov's theorem     

Importance measures for modular software with uncertain parameters

Importance measures provide a sense of the relative priorities of components and can be used to guide the allocation of resources for cost‐effective improvement of system reliability starting from the early phases. Uncertainties in model parameters, prevalent in the early phases, can introduce errors into these measures, and hence, importance assessment must account for these parametric uncertainties. In this paper, a framework for importance assessment of a software system within the context of its architecture is proposed. The framework includes two methods; the first one systematically quantifies the confidence intervals in the model parameters, and the second one offers an analytical approach for importance analysis. The two methods in conjunction address the issue of importance assessment in the face of parametric uncertainties. Illustration of the framework using a banking application demonstrates the value and benefits of the methodology. Copyright © 2009 John Wiley & Sons, Ltd.     

Factorizability conditions for multidimensional polynomials

In this paper, new results concerning the factorizability of multidimensional polynomials are presented. Necessary and sufficient conditions for the factorizability or separation of a givenm-D (m- dimensional) polynomial into: 1)m1-D polynomials, and 2) a number of multidimensional polynomials of appropriate dimensions are explicitly formulated.     

Invariance of a strict Hurwitz property for uncertain polynomials with dependent coefficients

This note is concerned with the invariance of strict Hurwitz property for uncertain polynomials having dependent coefficients. A feasible test criterion is provided which reduces the conservatism of the Kharitonov theorem.     

参数不确定机器人分散鲁棒跟踪控制

提出了一种新的参数不确定机器人分散控制器设计方法．首先将关节子系统的动力学模型分解为人工标称模型和非线性时变不确定模型两部分；然后分别设计相应的标称控制器和鲁棒补偿器．标称控制器使得标称闭环系统具有理想的跟踪性能；鲁棒补偿器可以抑制参数不确定和关节间非线性耦合等因素的影响，实现鲁棒跟踪．所设计的控制器只需要局部关节的位置反馈，具有易于实现和可在线调整的优点．仿真结果说明了该方法的有效性．     

Optimal-observer design for linear dynamical systems with uncertain parameters

This paper presents a design technique for the synthesis of robust observers for linear dynamical systems with uncertain parameters. The perturbations under consideration are modelled as unknown but bounded disturbances and an ellipsoidal set-theoretic approach is used to formulate the optimal-observer design problem. The optimal criterion introduced here is the minimization of the ‘size’ of the bounding ellipsoid of the estimation error. A necessary and sufficient condition for this optimal design problem is presented. The results are stated in terms of a reduced-order observer with constant gain matrix, which is then determined by solving a matrix Riccati-type equation. Furthermore, a gradient-search algorithm is presented to find the optimal solution when the free parameter that enters in the construction of the bounding ellipsoids of the estimation error is considered as a design parameter. The effectiveness of the proposed approach is illustrated through a numerical example.     

Stochastic control with uncertain macroeconomic parameters

An econometric model of the U.S. economy with random coefficients is solved as a stochastic control problem by augmenting the state vector with random coefficients, linearizing the resulting problem, and obtaining a feedback rule for the augmented problem. The performance of this augment closed loop rule is then compared to regular closed rule with Monte Carlo methods on one-random parameter and three-random parameter examples.     

Stability conditions for polytopes of polynomials

In considering the stability or performance of linear systems with uncertain parameters one is led to consider the simultaneous stability of families of polynomials. For a general stability region in the complex plane, the author gives a stability criterion for polytopes of polynomials in terms of the stability of a minimal number of corners and edges of the polytope. The testing set of edges and corners depends entirely on the edge directions of the polytope; hence the results are particularly applicable to problems with fixed directions, but varying lengths and positions of the edges. Applications to robust pole placement of uncertain systems and computation of worst case H_∞ norms are demonstrated     

Stability of polynomials under coefficient perturbation

Let the real polynomiala_{0}x^{n} + a_{1}x^{n-1} + ... + a_{n-1}x + a_{n}be stable and let the real numbersb_{k}, c_{k} geq 0, 0 leq k leq n, be given. We present a simple determinant criterion for finding the largestt_{0} geq 0such that the polynomialalpha_{0}x^{n} + alpha_{1}x^{n-1}+ ... +alpha_{n-1}x + alpha_{n}is stable for allalpha_{k} in (a_{k} - b_{k}t_{0}, a_{k} + C_{k}t_{0}) cup {a_{k}}, 0 leq k leq n. Several further observations allow us to reduce the computational cost considerably.     

Root regions of bounded coefficient polynomials

For fixed degree monic polynomials with real coefficients, the direct and inverse problems of root inclusion are denned. The direct problem is to find the infimal region Γ¹ _γof the C-plane that contains all roots of the bounded coefficient norm polynomials. The inverse problem is to define the maximal subregion Γ² _γ of Γ¹ _γ such that all polynomials with their roots in Γ² _γ are bounded norm coefficient polynomials. Those two problems are solved in the case of stable and totally unstable polynomials and the boundaries of Γ¹ _γ,Γ² _γ: regions are defined as branches of an algebraic function defined by the norm bound y. For general polynomials, the inverse problem is also solved for polynomials of any degree, whereas the direct problem is discussed in the case of third-order polynomials.     

参数摄动系统的鲁棒H ∞状态估计

基于Shaked提出的参数依赖型有界实引理，研究具有凸多面体参数摄动系统的鲁棒H∞状态估计问题．采用线性矩阵不等式技术，推导出此类不确定系统的全阶鲁棒H∞滤波器存在的充分条件，并将滤波器的设计转化为一个凸优化的求解问题．与传统的基于二次稳定的滤波方案相比，该滤波器设计方法具有较小的保守性．     

Robust stabilization for continuous-time systems with slowlytime-varying uncertain real parameters

The authors construct a class of parameter-dependent Lyapunov functions to guarantee robust stability in the presence of time-varying rate restricted plant uncertainty. Extensions to a class of time-varying nonlinear uncertainty that generalize the multivariable Popov criterion are also considered. These results are then used for controller synthesis to address the problem of robust stabilization in the presence of slowly time-varying real parameters     

Evaluating probabilistic models with uncertain model parameters

Probabilistic models are commonly used to evaluate quality attributes, such as reliability, availability, safety and performance of software-intensive systems. The accuracy of the evaluation results depends on a number of system properties which have to be estimated, such as environmental factors or system usage. Researchers have tackled this problem by including uncertainties in the probabilistic models and solving them analytically or with simulations. The input parameters are commonly assumed to be normally distributed. Accordingly, reporting the mean and variances of the resulting attributes is usually considered sufficient. However, many of the uncertain factors do not follow normal distributions, and analytical methods to derive objective uncertainties become impractical with increasing complexity of the probabilistic models. In this work, we introduce a simulation-based approach which uses Discrete Time Markov Chains and probabilistic model checking to accommodate a diverse set of parameter range distributions. The number of simulation runs automatically regulates to the desired significance level and reports the desired percentiles of the values which ultimately characterises a specific quality attribute of the system. We include a case study which illustrates the flexibility of this approach using the evaluation of several probabilistic properties.     

Hybrid multilevel programming with uncertain random parameters

Multilevel programming is developed for modeling decentralized decision-making processes. For different management requirements and risk tolerances of different-level decision-makers, the decision-making criteria applied in different levels cannot be always the same. In this paper, a hybrid multilevel programming model with uncertain random parameters based on expected value model (EVM) and dependent-chance programming (DCP), named as EVM–DCP hybrid multilevel programming, is proposed. The corresponding concepts of Nash equilibrium and Stackelberg–Nash equilibrium are given. For some special case, an equivalent crisp mathematical programming is proposed. An approach integrating uncertain random simulations, Nash equilibrium searching approach and genetic algorithm is designed. Finally, a numerical experiment of uncertain random supply chain pricing decision problem is given.     

Adaptive sliding-mode control for nonlinear systems with uncertain parameters.

This correspondence proposes a systematic adaptive sliding-mode controller design for the robust control of nonlinear systems with uncertain parameters. An adaptation tuning approach without high-frequency switching is developed to deal with unknown but bounded system uncertainties. Tracking performance is guaranteed. System robustness, as well as stability, is proven by using the Lyapunov theory. The upper bounds of uncertainties are not required to be known in advance. Therefore, the proposed method can be effectively implemented. Experimental results demonstrate the effectiveness of the proposed control method.     

不确定超混沌系统的反同步研究

研究了具有相同结构的超混沌系统的反同步问题。基于Lyapunov稳定性理论和自适应控制方法,给出了系统参数不确定时系统反同步的自适应控制律;通过对超混沌LV系统的数值仿真,验证了提出方案的有效性。     

An interactive satisficing approach for multi-objective optimization with uncertain parameters

Uncertain variables are used to describe the phenomenon where uncertainty appears in a complex system. For modeling the multi-objective decision-making problems with uncertain parameters, a class of uncertain optimization is suggested for the decision systems in Liu and Chen (2013), http://orsc.edu.cn/online/131020 which is called the uncertain multi-objective programming. In order to solve the proposed uncertain multi-objective programming, an interactive uncertain satisficing approach involving the decision-maker’s flexible demands is proposed in this paper. It makes an improvement in contrast to the noninteractive methods. Finally, a numerical example about the capital budget problem is given to illustrate the effectiveness of the proposed model and the relevant solving approach.     

参数不确定柔性机械手的终端滑模控制

针对参数不确定双臂柔性机械手系统, 提出一种基于遗传算法的终端滑模控制方法, 以实现其末端控制.基于输出重定义方法, 通过输入输出线性化, 将系统分解为输入输出子系统和内部子系统. 设计终端滑模控制策略,使输入输出子系统有限时间内收敛到零, 内部子系统变为零动态子系统; 采用遗传算法优化零动态子系统参数, 使其在平衡点附近渐近稳定. 根据Lyapunov稳定性理论算出末端输出位移的误差范围. 仿真结果证明该方法有效性.     

Locally optimal feedback strategy for non-linear systems with uncertain parameters

This paper broadens the classical optimal control approach to the optimal regulation of a non-measurable, but parametrized uncertainty. A locally optimal feedback strategy (LOFS) is derived by minimizing a measure of the performance index sensitivity with respect to the uncertainty parameter vector. In the state feedback case the LOFS can be characterized by an extension of the well-known Matrix-Riccati equation. Conditions for stability and finiteness of the resulting linear feedback law are derived for the stationary LQ case with uncertain parameters. Different numerical algorithms also covering the output feedback case are presented. Examples demonstrate the superior performance of the proposed feedback for problems with a significant parametric uncertainty.     

Robust stability conditions for DMC controller with uncertain time delay

For Networked Control Systems (NCSs), the conventional Dynamic Matrix Control (DMC) may not applicable due to the unknown transmission delay. The uncertain time delay was usually converted to constant time delay by using registers. This paper addresses the stability problem for single-input-single-output (SISO) linear NCSs with uncertain time delay via DMC controller. A novel DMC controller which is effective for such NCSs has been proposed. Applying Jury’s dominant coefficient lemma, the sufficient stability and stabilization conditions are presented. Finally, numerical examples are given to demonstrate the theoretical results.