editorial stochastic systems and control: theory and...

EditorialStochastic Systems and Control: Theory and Applications

Weihai Zhang,1 Honglei Xu,2 HuanqingWang,3 and Zhongwei Lin4

1College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China2Department of Mathematics and Statistics, Curtin University, Perth, WA, Australia3Department of Mathematics, Bohai University, Jinzhou, Liaoning 121000, China4State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University,Beijing 102206, China

Correspondence should be addressed to Weihai Zhang; w [email protected]

Received 20 November 2017; Accepted 21 November 2017; Published 27 December 2017

Copyright © 2017 Weihai Zhang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The objective of this special issue is to address recent researchtrends and developments in stochastic control systems andtheir applications to control, filtering, communication, man-ufacturing, fault detection, and systems biology. A substantialnumber of papers were submitted, and after a thoroughpeer review process, some related papers were selected to beincluded in this special issue. These papers collected in thisspecial issue highlight the contemporary topics in researchrelated to stochastic systems control theory and applicationsand will introduce readers to the latest advances in the field.

The paper by X. Li et al. presents a decentralized coor-dinated control of double fed induction generators basedon the neural interaction measurement observer. The pro-posed controller can be formulated as a mixed optimizationproblem with constraints of PI structure and regional poleplacement. Simulation results are presented to demonstratethe capabilities of the proposed control strategy.

The paper by X. Geng et al. considers A-diagnosabilityin distributed stochastic discrete event systems. A localmodel and global model are defined, and a synchronizedstochastic diagnoser is constructed.The authors also proposea necessary and sufficient condition for a distributed SDES tobe A-diagnosable.

The paper by J. Zhang et al. investigates a new stochasticchemostat model with two substitutable nutrients and onemicroorganism. Firstly, for the deterministic model, thethreshold for extinction or existence of the microorganismis obtained by analyzing the stability of the equilibrium.Thenthe threshold of the stochastic chemostat for the extinction

and the permanence in mean of the microorganism isexplored.

The paper by H. Huang analyzes one kind of linearquadratic stochastic control problem of forward backwardstochastic control system associated with Levy process. Weobtain the explicit form of the optimal control, then proveit to be unique, and get the linear feedback regulator byintroducing one kind of generalized Riccati equation. Finally,we discuss the solvability of the generalized Riccati equation,and its existence and uniqueness of the solutions are provedin a special case.

The paper by Y. Zhao and Y. Fu investigates the problemsof stability and stabilization for stochastic Markovian jumpsystems subject to partially unknown transition probabilitiesand multiplicative noise. By introducing the free-weighingmatrix method, the results obtained in this paper not onlyare less conservative than the existing ones but also canbe regarded as extensions of the corresponding results ofMarkovian jump systems without noise.

The paper by P. Shang and L. Kong discusses the mixedmatrix regressionmodel to deal with the complex matrix andvector data. Under some mild conditions, it is proved thatthe degrees of freedom of mixed matrix regression model arethe sum of the degrees of freedom of Lasso and regularizedmatrix regression.

The paper by G. Zhu et al. presents a neural networkprespecified performance control scheme for a class ofgeneric hypersonic flight vehicles with uncertain dynamicsand stochastic disturbance.Themain feature of the proposed

HindawiMathematical Problems in EngineeringVolume 2017, Article ID 4063015, 4 pageshttps://doi.org/10.1155/2017/4063015

https://doi.org/10.1155/2017/4063015

2 Mathematical Problems in Engineering

scheme is that only one parameter needs to be estimated ateach design step, so that the computational burden can begreatly reduced and the designed controller is much simpler.

The paper by M. Elloumi and S. Kamoun proposesan improved structural estimation procedure for large-scaleinterconnected nonlinear systems which are composed ofa set of interconnected SISO Hammerstein structures anddescribed by discrete-time stochastic models with unknowntime-varying parameters. An extensive Determinant Reportalgorithm is developed to determine the order of the process.An improved discrete-time technique based on RecursiveExtended Least Squares with Varying Time Delay methodis proposed to estimate the time delays of the consideredsystem. The developed theoretical analysis and simulationresults prove the validity and performance of the proposedalgorithms.

The paper by T. Hou et al. deals with the mixed controlproblem through the solvability of four coupled differencematrix-valued recursions for discrete-time infinite Markovjump systems. And a numerical example is given to illustrateits efficiency.

The paper by R. Caballero-Aguila et al. addresses the leastsquares centralized fusion estimation problem of discrete-time random signals from measured outputs. By an innova-tion approach and using the last observation that successfullyarrived when a packet is lost, a recursive algorithm isdesigned for the filtering estimation problem. The proposedalgorithm is easily implemented and does not require knowl-edge of the signal evolution model, as only the first- andsecond-order moments of the processes involved are used.

The paper by Z. Li et al. presents a novel fifth-degreecubature Kalman filter to improve the accuracy of real-timeorbit determination by ground-based radar. The simulationresults show that, compared with the traditional third-degreealgorithm, the proposed fifth-degree algorithm has a higheraccuracy of orbit determination.

The paper by C. Zhou et al. investigates a two-stagestochastic quadratic programming problem with inequalityconstraints. By quasi-Monte-Carlo-based approximations ofthe objective function, a feasible sequential system of linearequationsmethod is proposed.The convergence rate is locallysuperlinear under some additional conditions.

This paper by W. Sun et al. investigates the controlproblem of magnetic levitation system, in which velocityfeedback signal is influenced by stochastic disturbance.Single-degree-freedom magnetic levitation is regarded as anenergy-transform action device. Based on the Hamiltonianstructure, the control law of magnetic levitation system isdesigned by applying Lyapunov theory.

The paper by Z. Zheng et al. investigates preferentialrandom walks (PRW) on weighted complex networks. Byusing two different analytical methods, two exact expressionsare derived for the mean first passage time between twonodes. This work may provide a comprehensive approachfor exploring random walks on complex networks, especiallybiased random walks, which could help to better understandand tackle some practical problems such as search androuting on networks.

The paper by L. Zhang et al. presents multienergy hybridsystem structure and constructs a scheduling model withthe objective functions of maximum economic benefit andminimum power output fluctuation. Robust stochastic the-ory is introduced to describe uncertainty and propose amultiobjective stochastic scheduling optimization mode bytransforming constraint conditions with uncertain variables.

The paper by P. Wang et al. presents an efficient approx-imation of the Labeled Multi-Bernoulli Filter to performonline multitarget state estimation and track maintenanceefficiently. Then, a target posterior approximation techniqueis proposed to use a weighted single Gaussian componentrepresenting each individual target. Numerical results verifythat the proposed efficient approximation of the LMB filerachieves accurate tracking performance.

The paper byM. Liu et al. investigates a stochastic optimalcontrol problem where the control system is driven by Ito-Levy process. The necessary condition about existence ofoptimal control for stochastic system by using traditionalvariational technique under the assumption that controldomain is convex is proved. As an application to finance,an example of recursive consumption utility optimizationproblem is used to illustrate the practicability of our result.

The paper by H. Hu et al. considers a stock pricemodeled by a geometric-Brownian motion which featuresvolatility uncertainty to analyze the financial markets withvolatility uncertainty. A new arbitrage-free concept is utilizedto obtain the detailed results which give us an economicallybetter understanding of financial markets under volatilityuncertainty.

The paper by P. S. Kim proposes an alternative finitememory structure (FMS) smoother with a recursive formunder a least squares criterion using a forgetting factorstrategy. The proposed FMS smoother is shown to have goodinherent properties such as time-invariance, unbiasedness,and deadbeat. It is shown that the proposed FMS smoothercan be better than the existing FMS smoother for incorrectnoise covariance and the IMS smoother for temporaryuncertainties.

The paper by N. Yuguang et al. presents a novel methodcombining Markov chain model and generalized projectionnonnegative matrix factorization to detect and diagnose thefaults in industrial process. The proposed method is appliedto a 1000MW unit boiler process. The simulation resultsclearly illustrate the feasibility of the proposed method.

The paper by J. Kong et al. proposes a novel deep neuralnetwork model for prune reordering table. The reorderingmodel in PBMT by filtering reordering table is optimizedusing a recursive autoencoder model. The experimentalresults show that the proposed approach obtains highimprovement in BLEU score with lower scale of reorderingtable on two language pairs: English-Chinese and Uyghur-Chinese MT.

The paper by X. Cai et al. proposes a novel methodon selection of an initial covariance matrix and a horizonfor the Kalman filter to make sure that a sequence of theclosed-loop Kalman filters are stable as time-invariant filtersat subsequent time instant.The convergent properties and thestability conditions are less conservative since they provide

Mathematical Problems in Engineering 3

analytic results and are applicable to more common caseswhere the RDEs are not monotonic.

Thepaper byM.Cui et al. considers themodel and controlproblem of nonlinear active suspension in rough road. Byan appropriate transform, the model is transformed into alower triangular system, which can be used as backsteppingmethod. Then a controller is designed such that the meansquare of the state converges to an arbitrarily small neigh-borhood of zero by tuning design parameters.The simulationresults illustrate the effectiveness of the proposed scheme.

The paper by X. Leng et al. proposes a stochastic SIVSepidemic system with nonlinear saturated infection rateunder vaccination and investigates the dynamics predictedby the model. By using Ito’s formula and Lyapunov methods,this paper investigates the existence and uniqueness of globalpositive solution. It is shown that large stochastic noisescan lead to the extinction of epidemic diseases. Finally, thenumerical simulations demonstrate the performance of thetheoretical findings.

The paper by K. Nakade and H. Niwa discusses theeffect by the lead time quotation in an M/M/1 base stockmanufacturing-inventory queue into the customer’s utilityfunction.The numerical examples show that the optimal leadtime quotation policy for maximizing system’s average profithas low customer’s utility, and the other simple heuristicquotation policy leads to the greater expected values ofcustomers’ utility.

The paper by S. Li et al. constructs a new class of interestmodels considering stochastic behavior of interest rates infinancial market by compound Poisson process. Simulationsare used to illustrate the theoretical results and the effect ofparameters in interest model on actuarial present values isalso analyzed.

The paper by N. Duan et al. considers a more generalstochastic nonlinear time delay system driven by unknowncovariance noise and investigates its adaptive state-feedbackcontrol problem. By Lyapunov-Krasovskii functionals andadaptive backstepping, an adaptive state-feedback controlleris constructed by overcoming the negative effects broughtby unknown time delay and covariance noise. A simulationexample demonstrates the effectiveness of the proposedscheme.

The paper by J. Ma et al. considers an optimal liquidationby using the Almgren-Chriss market impact model on thebackground that the agents liquidate assets completely. Thestochastic component of the price process is eliminated fromthe mean-variance. The Nash equilibrium is considered asthe second-order linear differential equation with variablecoefficients. The existence and uniqueness of solutions areproved for the differential equation with two boundaries.Thenumerical examples and properties of the solution are given.

The paper by Y. Yi et al. studies a cooperative stochas-tic differential game of transboundary industrial pollutionbetween two asymmetric nations in infinite-horizon level.The feedbackNash equilibrium strategies of governments andindustrial firms are discussed. It is found that the govern-ments being cooperative in transboundary pollution controlwill set a higher pollution tax rate and make more pollutionabatement effort than when they are noncooperative.

The paper by L. Li et al. discusses stochastic multi-itemcapacitated lot-sizing problemswith andwithout setup carry-overs, S-MICLSP and S-MICLSP-L. A new fix-and-optimizeapproach is developed to solve the approximated models.Numerical experiments are performed on the instancesfollowing the nature of realistic steel products.

The paper by S. Kim et al. considers a multiperiodinventory control model in which a risk averse firm faces lossaverse customer’s uncertain demand and makes an inventoryreplenishment and pricing decision by maximizing the firm’sexpected utility.

The paper by M. Yu et al. considers the global expo-nential antisynchronization in mean square of memristiveneural networks with stochastic perturbation and mixedtime-varying delays. Two kinds of novel delay-dependentand delay-independent adaptive controllers are designed.On the basis of the differential inclusions theory, inequalitytheory, and stochastic analysis techniques, several sufficientconditions are obtained to guarantee the exponential antisyn-chronization between the drive system and response system.

The paper by X. Li et al. presents a novel multivariateBayesian control approachwhich enables the implementationof early fault detection for a helicopter gearboxwith costmin-imization maintenance policy under varying load. The effec-tive computational algorithm in the semi-Markov decisionprocess framework is designed to obtain the optimal controllimit. A comparison with the multivariate Bayesian controlchart based on hidden Markov model and the traditionalage-based replacement policy is given which illustrates theeffectiveness of the proposed approach.

The paper by L. Wang et al. presents the state space andtransition rate matrix corresponding to the 6-componentstar Markov repairable system with spatial dependence viaprobability analysis method. Several reliability indices, suchas the availability, the probabilities of visiting the safety, thedegradation, the alert, and the failed state sets, are obtainedby Laplace transform method and a numerical example isprovided to illustrate the results.

The paper by Q. Cao et al. discusses the low frequencyrandom load of a tractor. An innovative method is presentedfor theoretical shift schedule modification by the fuzzyalgorithm, based on the random load standard deviation andthe alteration rate of both steady state values of the load andof the throttle position. The simulation results demonstratedthat the modified shift schedule could discover the runningstate of the tractor.

The paper by S. Ji and X. Shi concerns the recursiveutility maximization problem for terminal wealth underpartial information. The considered problem under partialinformation is first transformed into the one under fullinformation. Then, the ignorance case and explicit saddlepoints of several examples are obtained. At last, when thegenerator of the recursive utility is smooth, the terminalperturbation method is applied to characterize the optimalterminal wealth.

Although the selected topics and published papers maynot represent all of the recent developments in the area, wehope that readers find the special issue helpful and useful.

4 Mathematical Problems in Engineering

Acknowledgments

We sincerely thank all of the reviewers for their valuablecomments and suggestions which have contributed greatly tothe quality of the special issue.

Weihai ZhangHonglei Xu

Huanqing WangZhongwei Lin

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