Issues in nonlinear stochastic grey box identification

Grey box identification refers to the practice of identifying dynamical systems in model structures exploiting partial prior information. This contribution reviews a method for stochastic grey box identification and surveys experiences and lessons of applying it to a number of industrial processes. Issues to be addressed include advantages and costs of introducing stochastics into the model, the question of what contribution must be expected from the model designer as opposed to what can be formalized in computer algorithms, and an outlook on future plans to resolve present shortcomings.     

I．O．T．旧梦成真

该文较详细地介绍了Ｉ．Ｏ．Ｔ管的发展历程，其特点及工作方式。     

Sampling average approximation method for a class of stochastic Nash equilibrium problems

We consider a class of stochastic Nash equilibrium problems (SNEP). Under some mild conditions, we reformulate the SNEP as a stochastic mixed complementarity problem (SMCP). We apply the well-known sample average approximation (SAA) method to solve the SMCP. We further introduce a semismooth Newton method to solve the SAA problems. The comprehensive convergence analysis is given as well. In addition, we demonstrate the proposed approach on a stochastic Nash equilibrium model in the wholesale gas–oil markets.     

Limit load and shakedown analysis of plastic structures under stochastic uncertainty

Problems from plastic analysis are based on the convex, linear or linearised yield/strength condition and the linear equilibrium equation for the stress (state) vector. In practice one has to take into account stochastic variations of several model parameters. Hence, in order to get robust maximum load factors, the structural analysis problem with random parameters must be replaced by an appropriate deterministic substitute problem. A direct approach is proposed based on the primary costs for missing carrying capacity and the recourse costs (e.g. costs for repair, compensation for weakness within the structure, damage, failure, etc.). Based on the mechanical survival conditions of plasticity theory, a quadratic error/loss criterion is developed. The minimum recourse costs can be determined then by solving an optimisation problem having a quadratic objective function and linear constraints. For each vector a(·) of model parameters and each design vector x, one obtains then an explicit representation of the “best” internal load distribution F^∗. Moreover, also the expected recourse costs can be determined explicitly. Consequently, an explicit stochastic nonlinear program results for finding a robust maximal load factor μ^∗. The analytical properties and possible solution procedures are discussed.     

RAZUMIKHIN-TYPE THEOREMS OF NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.     

A mathematical model for vehicle routing problem under endogenous uncertainty

In this study, a multistage stochastic programming (SP) model is presented for a variant of single-vehicle routing problem with stochastic demands from a dynamic viewpoint. It is assumed that the actual demand of a customer becomes known only when the customer is visited. This problem falls into the category of SP with endogenous uncertainty and hence, the scenario tree is decision-dependent. Therefore, nonanticipativity of decisions is ensured by conditional constraints making up a large portion of total constraints. Thus, a novel approach is proposed that considerably reduces the problem size without any effect on the solution space. Computational results on some test problems are reported.     

Stochastic differential equations driven by a Wiener process and fractional Brownian motion: Convergence in Besov space with respect to a parameter

A stochastic differential equation involving both a Wiener process and fractional Brownian motion, with nonhomogeneous coefficients and random initial condition, is considered. The coefficients and initial condition depend on a parameter. The assumptions on the coefficients and the initial condition supplying continuous dependence of the solution on a parameter, with respect to the Besov space norm, are established.     

Identification and quantification of different vapours using a single polymer chemoresistor and the novel dual transient temperature modulation technique

This paper presents a novel signal processing technique for a square wave temperature modulated carbon black/polymer composite sensor. The technique consists of only two mathematical operations: summing the off- and on-transients of the conductance signals, and subtracting the steady-state conductance signal. The technique has been verified through its application to a carbon black/polyvinylpyrrolidone composite chemoresistor. Identification of water, methanol and ethanol vapours was successfully demonstrated using the peak time of the resultant curves. Furthermore, quantification of those vapours was found to be possible using the height of the peak heights, which was linearly proportional to concentration. The technique does not require zero-gas calibration and thus is superior to previously reported techniques.     

Existence of optimal controls for systems driven by FBSDEs

We prove the existence of optimal relaxed controls as well as strict optimal controls for systems governed by non linear forward-backward stochastic differential equations (FBSDEs). Our approach is based on weak convergence techniques for the associated FBSDEs in the Jakubowski S-topology and a suitable Skorokhod representation theorem.     

Combinatorial optimization under uncertainty

In this paper, the general problem of Euclidean combinatorial optimization under uncertainty is formulated for the first time and the concepts of a stochastic multiset, a multiset of fuzzy numbers, a stochastic Euclidean combinatorial set, and general Euclidean combinatorial set of fuzzy stochastic numbers that combines the properties of both types of uncertainty are introduced. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 35–44, September–October 2008.