Decentralized Adaptive Robust Tracking and Model Following for Large-Scale Systems Including Delayed State Perturbations in the Interconnections

The problem of decentralized robust tracking and model following is considered for a class of uncertain large-scale systems including delayed state perturbations in the interconnections. In this paper, it is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances are unknown. A modified adaptation law with σ-modification is introduced to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a class of decentralized local memoryless state feedback controllers is constructed for robust tracking of dynamical signals. The proposed decentralized adaptive robust tracking controllers can guarantee that the tracking errors between each time-delay subsystem and the corresponding local reference model without time-delay decrease uniformly asymptotically to zero. Finally, a numerical example is given to demonstrate the validity of the results.     

Robustness and applicability of Markov chain Monte Carlo algorithms for eigenvalue problems

In this paper we analyse applicability and robustness of Markov chain Monte Carlo algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices.

Almost Optimal Monte Carlo (MAO) algorithms for solving eigenvalue problems are formulated. Results for the structure of both – systematic and probability error are presented. It is shown that the values of both errors can be controlled independently by different algorithmic parameters. The results present how the systematic error depends on the matrix spectrum. The analysis of the probability error is presented. It shows that the close (in some sense) the matrix under consideration is to the stochastic matrix the smaller is this error. Sufficient conditions for constructing robust and interpolation Monte Carlo algorithms are obtained. For stochastic matrices an interpolation Monte Carlo algorithm is constructed.

A number of numerical tests for large symmetric dense matrices are performed in order to study experimentally the dependence of the systematic error from the structure of matrix spectrum. We also study how the probability error depends on the balancing of the matrix.     

Nonparametric predictive pairwise comparison for real-valued data with terminated tails

This paper presents a statistical method for comparison of two groups of real-valued data, based on nonparametric predictive inference (NPI), with the tails of the data possibly terminated, leading to small values being left-censored and large values being right-censored. Such tails termination can occur due to several reasons, including limits of detection, consideration of outliers, and specific designs of experiments. NPI is a statistical approach based on few assumptions, with inferences strongly based on data and with uncertainty quantified via lower and upper probabilities. We present NPI lower and upper probabilities for the event that the value of a future observation from one group is less than the value of a future observation from the other group, and we discuss several special cases that relate to well-known statistical problems.     

Cascading: an adjusted exchange method for robust conic programming

It is well known that the robust counterpart introduced by Ben-Tal and Nemirovski (Math Oper Res 23:769–805, 1998) increases the numerical complexity of the solution compared to the original problem. Kočvara, Nemirovski and Zowe therefore introduced in Kočvara et al. (Comput Struct 76:431–442, 2000) an approximation algorithm for the special case of robust material optimization, called cascading. As the title already indicates, we will show that their method can be seen as an adjustment of standard exchange methods to semi-infinite conic programming. We will see that the adjustment can be motivated by a suitable reformulation of the robust conic problem.      

Robust optimization using computer experiments

During metamodel-based optimization three types of implicit errors are typically made. The first error is the simulation-model error, which is defined by the difference between reality and the computer model. The second error is the metamodel error, which is defined by the difference between the computer model and the metamodel. The third is the implementation error. This paper presents new ideas on how to cope with these errors during optimization, in such a way that the final solution is robust with respect to these errors. We apply the robust counterpart theory of Ben-Tal and Nemirovsky to the most frequently used metamodels: linear regression and Kriging models. The methods proposed are applied to the design of two parts of the TV tube. The simulation-model errors receive little attention in the literature, while in practice these errors may have a significant impact due to propagation of such errors.     

Robust a posteriori error estimation for the nonconforming Fortin-Soulie finite element approximation

We obtain a computable a posteriori error bound on the broken energy norm of the error in the Fortin-Soulie finite element approximation of a linear second order elliptic problem with variable permeability. This bound is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the error.

     

Robust portfolio selection with uncertain exit time using worst-case VaR strategy

To deal with the robust portfolio selection problem where only partial information on the exit time distribution and on the conditional distribution of portfolio return is available, we extend the worst-case VaR approach and formulate the corresponding problems as semi-definite programs. Moreover, we present some numerical results with real market data.     

结构稳健性设计与考虑不确定因素的优化设计的比较

用典型的三杆桁架结构设计问题，进行了结构稳健性设计与考虑不确定因素的优化设计的比较，通过用蒙特卡罗模拟法对设计结果的结构可靠性计算，表明两种设计在提高结构可靠性上是一致的，但结构稳健性设计更具有有效控制结构特性散布的优点。     

Minimization Algorithms Based on Supervisor and Searcher Cooperation

In the present work, we explore a general framework for the design of new minimization algorithms with desirable characteristics, namely, supervisor-searcher cooperation. We propose a class of algorithms within this framework and examine a gradient algorithm in the class. Global convergence is established for the deterministic case in the absence of noise and the convergence rate is studied. Both theoretical analysis and numerical tests show that the algorithm is efficient for the deterministic case. Furthermore, the fact that there is no line search procedure incorporated in the algorithm seems to strengthen its robustness so that it tackles effectively test problems with stronger stochastic noises. The numerical results for both deterministic and stochastic test problems illustrate the appealing attributes of the algorithm.     

Robust hurwitz property of bivariate polynomials in the space of Markov parameters

Markov parameters and the associated stability criterion were first introduced for continuous-time real polynomials. Recently, robust stability of such polynomials was considered in Markov parameters space, where efficient robust stability tests were obtained based on the Markov theorem. This motivated the authors to extend the above idea, and develop Markov parameters and the associated stability criterion for more general types of polynomials such as complex continuous-time as well as real and complex discrete-time polynomials. In this paper a procedure is given for evaluating the maximum allowable perturbations in the Markov parameters of a complex coefficient univariate as well as real coefficient bivariate polynomials so that the strict Hurwitz property remains invariant.