EditorialMathematical Theories and Applications forNonlinear Control Systems

Xue-Jun Xie ,1 Ju H. Park ,2 Hiroaki Mukaidani,3 andWeihai Zhang 4

1 Institute of Automation, Qufu Normal University, Qufu, China2Department of Electrical Engineering, Yeungnam University, Kyongsan, Republic of Korea3Graduate School of Engineering, Hiroshima University, Higashihiroshima, Japan4College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China

Correspondence should be addressed to Xue-Jun Xie; xuejunxie@126.com

Received 31 March 2019; Accepted 31 March 2019; Published 10 April 2019

Copyright © 2019 Xue-Jun Xie 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.

Nonlinear control is without doubt a very popular researchfield in modern control theory. Compared with linear sys-tems, nonlinear control has more applications in practice,and the related problems of nonlinear control exhibit morecomplexity. Although nonlinear control theory and applica-tion have made great progress in recent years, there are stilla lot of new and challenging problems existing in the areasof theory analysis and applications, which cover the fieldsof multiobjective control, design of regulating and trackingsystems, fault estimation, nonlinear robust 𝐻

∞control and

filtering, stability and stabilization, etc.These problems meritfurther study by using more advanced theories and tools.

This special issue will focus on nonlinear control sys-tems together with their applications to control, filtering,communication, manufacturing, fault detection, and systemsbiology. The collection of papers with different areas of non-linear systems clearly points to the need for communicationbetween researches of these areas.

The paper entitled “A Time-Replacement Policy for Mul-tistate Systems with Aging Components under Maintenance,from a Component Perspective” by C.-H. Huang and C.-H.Wang studiesmultistate systems (MSSs)with agingmultistatecomponents (MSCs) to construct a time-replacement policyand determine the optimal time. Traditional mathematicscannot acquire accurate explicit expressions. To overcomethis difficulty, this paper uses Markov reward models and thebound approximation approach to assess rewards of MSSswith MSCs, including such things as total maintenance costsand the benefits of the system staying in acceptable workingstates.

R. Li et al. in the paper entitled “Research on Instabil-ity Boundaries of Control Force for Trajectory CorrectionProjectiles” propose a novel method to derive instabilityboundaries for the control force magnitude. By introducingthe concept of angular compensation matrix, the exteriorballistic linearized equations considering control force areestablished. The necessary prerequisite for a stable flightunder control is given by the Routh stability criterion. Theinstability boundaries for the control force magnitude arederived.

The paper by G. Liu et al. entitled “Dynamical Analysisand Optimal Harvesting Strategy for a Stochastic DelayedPredator-Prey Competitive System with Levy Jumps” devel-ops a theoretical framework to investigate optimal harvestingcontrol for stochastic delay differential systems. The authorsfirst propose a novel stochastic two-predator and one-preycompetitive system subject to time delays and Levy jumps.Some sufficient conditions for persistence in mean andextinction of three species are obtained by using the stochas-tic qualitative analysis method. The optimal harvesting effortand the maximum of expectation of sustainable yield arederived from the Hessian matrix method and optimal har-vesting theory of delay differential equations.

The paper entitled “Nonlinear Hybrid Multipoint Modelof High-Speed Train with Traction/Braking Dynamic andSpeed Estimation Law” by C. Jia et al. establishes a nonlin-ear hybrid multipoint model (NHMPM) for a high-speedtrain (HST) with the traction/braking dynamic and speedestimation law. A full-order flux observer is designed byusing regional pole assignment theory to calculate the

HindawiMathematical Problems in EngineeringVolume 2019, Article ID 2065786, 6 pageshttps://doi.org/10.1155/2019/2065786

2 Mathematical Problems in Engineering

electromagnetic torque. The basic running resistance forceis reformulated by considering the aerodynamic drag distri-bution characteristics, and the nonlinear coupling force isanalyzed as well.

F. Ma et al. in the paper entitled “Start-Up ProcessModelling of Sediment Microbial Fuel Cells Based on DataDriven” study a typical microbial fuel cell, called sedimentmicrobial fuel cells (SMFCs). This paper uses online mon-itoring technology to accurately measure the temperature,pH, and voltage of the microbial fuel cell during the start-upprocess. Experimental results show that the purpose ofrapid growth of power production can be achieved at theinitial stage of SMFC. At the beginning of SMFC, when thetemperature changes drastically, pH will change the samefirst, and then there will be a certain degree of rebound. In themiddle stage of SMFC start-up, even if the temperature willreturn to normal after the change, a continuous temperaturedrop in a short time will lead to a continuous decrease in pHvalue.

The paper by H. Kong and B. Yu entitled “A MovingObject Indoor Tracking Model Based on Semiactive RFID”studies the weak anti-interference and low accuracy problemof moving object indoor tracking based radio frequencyidentification devices (RFID) and presents a moving objectindoor tracking model based on semiactive RFID. Thismodel acquires scene location information through RFIDlow frequency triggers preinstalled and adopts an improvedparticle filter algorithm, which can increase the diversity ofthe particles, overcome the particle impoverishment, andreduce the tracking error.

J. An et al. in the paper entitled “Iterative LearningControl for Nonlinear Weighing and Feeding Process” usea piecewise linearization method for the nonlinear problemand discuss the application of iterative learning control in theweighing and feeding process. The nonlinear problem andthe repeatability are discussed based on dynamic analysis ofthe weighing and feeding process. A linear state space modelis established with a piecewise linearization method, anditerative learning controller is presented by utilizing repetitivecharacteristics.

The paper by Y. Sun et al. entitled “A High-PrecisionRotor Position and Displacement Prediction MethodSpecially for Bearingless Permanent Magnet SynchronousMotor” studies a rotor displacement and position predictionmethod based on a kernel extreme learning machine. Thehigh performance sensorless performance of the bearinglesspermanent magnet synchronous motor (BPMSM) is themain direction to improve the reliability of the drive systemand reduce the cost of the system. On the basis of themathematical model of BPMSM, this method predicts theposition and displacement of the rotor according to thecurrent and flux linkage of suspension windings and torquewindings by a kernel extreme learning machine (KELM).

E. Kose and A. Muhurcu in the paper entitled “Compara-tive Controlling of the Lorenz Chaotic SystemUsing the SMCand APP Methods” provide two different controller modelsfor the Lorenz chaotic system. Adaptive pole placementand sliding mode control (SMC) methods are proposed forthe establishment of the continuous time Lorenz chaotic

system. An improved controller structure is developed firsttheoretically for both the controller methods and thentested practically using the numerical samples. During theestablishment of the adaptive pole placement method forthe Lorenz chaotic system, various stages were applied. Thechaotic system reached an equilibrium point by using boththe SMC and adaptive pole placement methods.

The paper entitled “On an Application of the AbsoluteStability Theory to Sampled-Data Stabilization” by A. N.Churilov considers a nonlinear Lur’e-type plant with a sectorbound nonlinearity. The plant is stabilized by a discrete-timefeedback signal with a nonperiodic uncertain sampling. Thesampling control function is nonlinear and also obeys somesectoral constraints at discrete (sampling) times. The linearmatrix inequality (LMI) conditions for the stability of theclosed-loop system are obtained.

H.-M. Lee et al. in the paper entitled “Further Resultson Sampled-Data Synchronization for Complex DynamicalNetworks with Time-Varying Coupling Delay” deal with thesampled-data synchronization problem for complex dynam-ical networks (CDNs) with time-varying coupling delay.The two-sided free-weighting stabilization method is utilizedwith a novel looped functional by taking the information ofthe present sampled states and next sampled states, whichcan more precisely account for the sawtooth shape of thesampling delay. The quadratic generalized free-weightingmatrix inequality (QGFWMI) is utilized to calculate theupper limit of the integral term. Based on the novel loopedfunctional and QGFWMI, improved conditions of stabil-ity are derived from forms of linear matrix inequalities(LMIs).

The paper by G. Zhao entitled “Modeling and StabilityAnalysis for Markov Jump Networked Evolutionary Games”investigates the algebraic formulation and stability analysisfor a class of Markov jump networked evolutionary games byusing the semitensor productmethod and presents a numberof new results. A proper algorithm is constructed to convertthe given networked evolutionary games into an algebraicexpression. Based on the algebraic expression, the stabilityof the given game is analyzed and an equivalent criterion isgiven.

X. Li et al. in the paper entitled “Exponential Stabilityof Antiperiodic Solution for BAM Neural Networks withTime-Varying Delays” consider a kind of BAM neural net-works with leakage delays in the negative feedback termsand time-varying delays in activation functions. By con-structing a suitable Lyapunov function and using inequalitytechniques, some sufficient conditions to ensure the existenceand exponential stability of antiperiodic solutions of theseneural networks are derived.

Y. Sun et al. entitled in the paper “Maximum PowerPoint Tracking of DFIG with DC-Based Converter SystemUsing Coordinated Feedback Linearization Control” presenta coordinated feedback linearization strategy (CFLS) for aDC-based doubly fed induction generator (DFIG) systemto track the maximum power point. The stator and rotorof the DFIG are connected to the DC grid directly by twovoltage source converters. Compared with a traditional DFIGsystem, the DC-based DFIG system has more system inputs

Mathematical Problems in Engineering 3

and coupling, which increases the difficulty of vector controlstrategy.

The paper by Y. Wang et al. entitled “Fractional-OrderAdaptive Backstepping Control of a NoncommensurateFractional-Order Ferroresonance System” applies fractionalcalculus to establish a novel fractional-order ferroresonancemodel with fractional-order magnetizing inductance andcapacitance. A novel fractional-order adaptive controlleris designed in terms of the fractional Lyapunov stabilitytheorem. The proposed control strategy requires only onecontrol input and can force the output of the chaotic systemto track the reference signal asymptotically.

The paper entitled “Hot Spot Data Prediction ModelBased on Wavelet Neural Network” by M. Zhang and W.Chen improves the performance of data migration betweena solid-state hard disk and hard disk. The novel hybridmultilevel storage system will be popular with SSD beingintegrated into traditional storage systems.Thehot data blockprediction model based on a wavelet neural network is builtand trained by using historical data. Experimental resultsshow that the proposed model has better accuracy and fasterlearning speed than the BP neural network model. It hasbetter generalization ability and robustness. This model canbe applied to the data migration of distributed hybrid storagesystems to improve performance.

X. Zhao et al. in the paper entitled “Optimization Problemof Insurance Investment Based on Spectral RiskMeasure andRAROC Criterion” introduce spectral risk measure (SRM)into the optimization problem of insurance investment. Theauthors establish an optimization model aiming at maximiz-ing risk-adjusted return of capital (RAROC) involved withspectral risk measure. The theoretical result is derived andempirical study is displayed under different riskmeasures anddifferent confidence levels comparatively. The result showsthat risk attitude has a significant impact on investment strat-egy. With the increase of risk aversion factor, the investmentratio of risk asset correspondingly reduces.

The paper entitled “Optimal Control Based on the Poly-nomial Least Squares Method” by C. Bota et al. presents anapproach for computing an optimal control law based onthe Polynomial Least Squares Method (PLSM). The initialoptimal control problem is reformulated as a variationalproblem whose corresponding Euler-Lagrange equation issolved by using the PLSM. A couple of examples emphasizethe accuracy of the method.

The paper by Y. Ren et al. entitled “Research on Time-Space Fractional Model for Gravity Waves in BaroclinicAtmosphere” derives the integer order mKdV equation todescribe the gravity solitary waves which occur in the baro-clinic atmosphere. By employing the semi-inverse and vari-ational method, a new model under the Riemann-Liouvillederivative definition is obtained. The symmetry analysis andthe nonlinear self-adjointness of the space-time fractionalmKdV (STFmKdV) equation are carried out and the con-servation laws are analyzed. By adopting the exp(−Φ(𝜉))method, five different solutions of the STFmKdVequation areobtained.

S. Kong et al. in the paper entitled “Estimation andFault Diagnosis of Lithium-Ion Batteries: A Fractional-Order

System Approach” investigate the estimation and fault diag-nosis of a fractional-order lithium-ion battery system. Twosimple and common types of observers are designed toaddress the design of fault diagnosis and estimation forthe fractional-order systems. Fractional-order Luenbergerobservers are employed to generate residuals which are usedto investigate the feasibility of model based fault detec-tion and isolation. The notion of stability in the sense ofMittag-Leffler is first introduced to discuss the state estima-tion error dynamics. The design of the Luenberger observeras well as the sliding mode observer can accomplish faultdetection, fault isolation, and estimation. The effectiveness ofthe proposed strategy on a three-cell battery string system isdemonstrated.

The paper by C.-Q. Ma and W.-G. Sun entitled “BipartiteConsensus for Multiagent Systems via Event-Based Control”studies bipartite consensus for first-ordermultiagent systems.To improve resource utilization, event-based protocols areconsidered for bipartite consensus. A new type of control gainis designed in the proposed protocols. By appropriate selec-tion of control gains, the convergence rate of the closed-loopsystem can be adjusted. It can be found that the system willnot show Zeno behavior.

The paper entitled “𝐻∞

Control for Nonlinear InfiniteMarkov Jump Systems” by Y. Liu and T. Hou discusses theinfinite horizon 𝐻

∞control problem for a class of nonlin-

ear stochastic systems with state, control, and disturbancedependent noise. The jumping parameters are modeled as aninfinite-stateMarkov chain. Based on the solvability of a set ofcoupled Hamilton-Jacobi inequalities (HJIs), the exponentialmean square 𝐻

∞controller for the considered nonlinear

stochastic systems is obtained.Y. Chen et al. in the paper entitled “A New Robust Non-

fragile Controller Design Scheme for a Class of Hybrid Sys-tems through Piecewise AffineModels” investigate the robust𝐻∞

nonfragile control problem for a class of discrete-timehybrid systems based on piecewise affine models. By employ-ing a state-control augmentation methodology, some newsufficient conditions for the controller synthesis are for-mulated based on piecewise Lyapunov functions (PLFs).Controller gains can be obtained via solving a set of linearmatrix inequalities.

W. Hu in the paper entitled “ANew Stability Criterion forNeutral Stochastic Delay Differential Equations with Marko-vian Switching” investigates a new stability theorem forneutral stochastic delay differential equations with Marko-vian switching. By applying the stochastic analysis techniqueand Razumikhin stability approach, a novel criterion of the𝑝th moment exponential stability is derived for the relatedsystems. The feature of the criterion shows that the estimatedupper bound for the diffusion operator of the Lyapunovfunction is allowed to be indefinite, even if it is unbounded,which can loosen the constraints of the existing results.

Based on the adaptive sliding mode control technique, J.Zhao et al. in the paper entitled “A Novel Nonlinear FaultTolerant Control for Manipulator under Actuator Fault” pro-pose a fault tolerant control (FTC) scheme for a manipulatorwith actuator fault. The dynamic model of the manipulator isintroduced and its actuator faultymodel is established. A fault

4 Mathematical Problems in Engineering

tolerant controller is designed, in which both the parametersof actuator fault and external disturbance are estimated andupdated by online adaptive technology.

The paper entitled “Finite-Time Stabilization for Stochas-tic Inertial Neural Networks with Time-Delay via NonlinearDelay Controller” by D. Li et al. pays close attention tothe problem of finite-time stabilization related to stochasticinertial neural networks with or without time delay. Byestablishing a proper Lyapunov-Krasovskii functional andmaking use of matrix inequalities, some sufficient con-ditions on finite-time stabilization are obtained and thestochastic settling-time function is also estimated. In orderto achieve the finite-time stabilization, both delayed andnondelayed nonlinear feedback controllers are designed,respectively.

J. A. Colunga et al. in the paper entitled “Predefined-TimeConsensus of Nonlinear First-Order Systems Using a TimeBase Generator” propose a couple of consensus algorithmsformultiagent systems.Theproposed consensus protocols arebased on the so-called time base generators (TBGs), whichare time-dependent functions used to build time-varyingcontrol laws. One of the proposed protocols is based onthe super-twisting controller, providing robustness againstdisturbances while maintaining the predefined-time conver-gence property. It is shown that the proposed TBG protocolsrepresent an advantage not only in the possibility to definea settling time but also in providing smoother and smallercontrol actions than existing finite-time, fixed-time, andpredefined-time consensus.

The paper entitled “On Leaderless and Leader-FollowingConsensus for Heterogeneous Nonlinear Multiagent Systemsvia Discontinuous Distributed Control Protocol” by F. Wangand Y. Yang concerns the consensus of heterogeneous non-linear multiagent systems via distributed control. Both thecases of leaderless and leader-following consensus are sys-tematically investigated. Different from some existing results,completed consensus can be reached in this paper amongheterogeneous multiagent network instead of bounded con-sensus. A novel distributed control protocol is proposed, andsome general consensus criteria are derived for multiagentsystems without a leader.

The paper by X. Lin et al. entitled “𝐻∞

Robust TrackingControl of Stochastic T-S Fuzzy Systems with Poisson Jumps”designs a robust adaptive 𝐻

∞tracking control for nonlinear

stochastic systems with both Brownian motion and Poissonjumps, which is based on Takagi-Sugeno (T-S) type fuzzytechniques. By using the fuzzy systems to approximate thenonlinear systems, an adaptive fuzzy control is employed toachieve the desired 𝐻

∞tracking performance for stochastic

systems with exogenous disturbance.The paper by C. Guo and K. Zhang entitled “Global

Output Feedback Stabilization of Nonlinear Systems witha Time-Varying Power and Unknown Output Function”studies the problem of global output feedback stabilizationfor a class of nonlinear systems with a time-varying powerand unknown output function. For nonlinear systems witha time-varying power and unknown continuous outputfunction, by constructing a new nonlinear reduced-orderobserver together with adding a power integrator method,

a new function to determine the maximal open sector Ωof output function is given. As long as the output functionbelongs to any closed sector included in Ω, it is shownthat the equilibrium point of the closed-loop system can beguaranteed to be globally uniformly asymptotically stable byan output feedback controller.

Y. Guan and X. Song in the paper entitled “UnbiasedMinimum Variance Estimation for Discrete-Time Systemswith Measurement Delay and Unknown Measurement Dis-turbance” address the state estimation problem for stochasticsystems with unknown measurement disturbances any priorinformation of which is unknown and which has mea-surement delay resulting from the inherent limited band-width. For such complex systems, the Kalman-like one-steppredictor independent of unknown measurement distur-bances is designed based on the linear unbiased minimumvariance criterion and the reorganized innovation analysisapproach.

The paper entitled “Trajectory Design and TrackingControl for Nonlinear Underactuated Wheeled InvertedPendulum” by S. Gong et al. studies an underactuatedwheeled inverted pendulum (UWIP) system. The motionplanning problem for this nonlinear system is difficult tosolve because of the existence of an uncontrollable manifoldin the configuration space. A method of designing motiontrajectory for this underactuated system is presented. Thetracking control of the UWIP for the constructed trajectoryis also studied.

H. Wang and L. Zhao in the paper entitled “A Nonho-mogeneous Multivariable Grey Prediction NMGM Model-ing Mechanism and Its Application” propose a novel non-homogeneous multivariable grey prediction model termedNMGM(𝑎, 𝑚, 𝑘𝛼) to deal with those data sequences thatare not in accord with homogeneous index trend. Basedon grey prediction theory, by the least squares method andsolutions of differential equations, the modeling mechanismand time response function of the proposed model areexpounded. A case study demonstrates that the novel modelprovides preferable prediction performance compared withthe traditional MGM(1, 𝑚)model.

The paper by L. Wang et al. entitled “Adaptive FuzzyCommand Filtered Control for Chua’s Chaotic System” pro-poses the command filtered adaptive fuzzy backsteppingcontrol (AFBC) approach for Chua’s chaotic system withexternal disturbance. Based on two proposed first-ordercommand filters, the convergence of tracking errors as wellas the problem of “explosion of complexity” in the traditionalbackstepping design procedure is solved. Fuzzy logic systems(FLSs) are used to identify the system uncertainties in realtime.The proposed controller can guarantee that all signals inthe closed-loop system remain bounded, and tracking errorsconverge to a small region eventually.

The paper entitled “A New Approach to Adaptive Stabi-lization of Stochastic High-Order Nonholonomic Systems”by G. Li and K. Zhang studies the problem of adaptivestabilization for a class of stochastic high-order nonholo-nomic systems. Under the weaker assumptions, by con-structing the appropriate Lyapunov function and combiningthe sign function technique, an adaptive state feedback

Mathematical Problems in Engineering 5

controller is designed to guarantee global asymptotic sta-bility in probability of the closed-loop system. The effec-tiveness of the controller is demonstrated by a mechanicalsystem.

D. Liu et al. in the paper entitled “Stochastic StabilityAnalysis of Coupled Viscoelastic Systems with NonviscouslyDamping Driven by White Noise” investigate stochasticstability of a coupled viscoelastic system with nonviscousdamping driven by white noise through moment Lyapunovexponents. By using the coordinate transformation, coupledIto stochastic differential equations are obtained. The prob-lem of the moment Lyapunov exponent is transformed tothe eigenvalue problem, and then the second-perturbationmethod is used to derive the moment Lyapunov exponent ofthe coupled stochastic system.

The paper by X. Qin entitled “The Adaptive NeuralControl for a Class of High-Order Uncertain StochasticNonlinear Systems” studies the problem of the adaptiveneural control for a class of high-order uncertain stochasticnonlinear systems. By using some techniques such as thebackstepping recursive technique, Young’s inequality, andapproximation capability, a novel adaptive neural controlscheme is constructed. The proposed control method canguarantee that the signals of the closed-loop system arebounded in probability, and only one parameter needs to beupdated online.

The paper entitled “Adaptive Parallel Simultaneous Sta-bilization of a Class of Nonlinear Descriptor Systems viaDissipative Matrix Method” by L. Sun and R. Yang inves-tigates the adaptive parallel simultaneous stabilization androbust adaptive parallel simultaneous stabilization problemsof a class of nonlinear descriptor systems via the dissipativematrix method. Under an output feedback law, two non-linear descriptor systems are transformed into two nonlin-ear differential-algebraic systems by nonsingular transfor-mations, and a sufficient impulse-free condition is givenfor the two resulting closed-loop systems. Based on thedissipative system, an adaptive parallel simultaneous stabi-lization controller and a robust adaptive parallel simultaneousstabilization controller are designed for the two systems.

Motivated by the quorum-sensing mechanism of bac-teria, J. Zhang et al. in the paper entitled “Outer Syn-chronization of a Modified Quorum-Sensing Network viaAdaptive Control” modify the network model by addingunknown parameters and noise disturbances. There existthree unknown parameters, and updating laws are pre-sented to identify the unknown parameters with help ofthe Lyapunov stability theory. The negative effects of noisedisturbances are also compensated for by designing adaptivecontrollers.

The paper by X. Gao et al. entitled “A Common ValueExperimentation with Multiarmed Bandits” studies valuecommon experimentationwithmultiarmed bandits and givesan application about the experimentation.The second deriva-tive of value functions at cutoffs is investigated when an agentswitches action withmultiarmed bandits.TheMarkov perfectequilibrium and the socially effective allocation in K-armedmarkets are also discussed.

L. Wang et al. in the paper entitled “Adaptive Fuzzy Out-put FeedbackControl for Partial State ConstrainedNonlinearPure Feedback Systems” address the adaptive fuzzy outputfeedback control problem for a class of pure feedback systemswith partial state constraints. The fuzzy state observers aredesigned to estimate the unmeasured state while the fuzzylogic systems are used to approximate the unknown nonlin-ear functions. The proposed adaptive fuzzy output feedbackcontroller can guarantee that the partial state constraints arenot violated, and all closed-loop signals remain bounded byuse of Barrier Lyapunov Functions (BLFs).

The paper entitled “Adaptive Synchronization for Uncer-tain Delayed Fractional-Order Hopfield Neural Networksvia Fractional-Order Sliding Mode Control” by B. Mengand X. Wang studies adaptive synchronization for a classof uncertain delayed fractional-order Hopfield neural net-works (FOHNNs) with external disturbances. For theunknown parameters and external disturbances of thedelayed FOHNNs, some adaptive estimations are designed. Afractional-order switched sliding surface is proposed for thedelayed FOHNNs. According to the fractional-order exten-sion of the Lyapunov stability criterion, a fractional-ordersliding mode controller is constructed to guarantee that thesynchronization error of the two uncertain delayed FOHNNsconverges to an arbitrary small region of the origin.

The paper by J. Zhao and F. Meng entitled “StabilityAnalysis of Solutions for a Kind of Integro-Differential Equa-tions with a Delay” analyzes the stability of the zero solutionfor second-order integrodifferential equations with a delay.By constructing the Lyapunov functional, the correspondingsufficient conditions on stability of the zero solution for twointegrodifferential equations are provided.

D. Zhu and C. Yin in the paper entitled “Stochastic Opti-mal Control of Investment and Dividend Payment Modelunder Debt Control with Time-Inconsistency” consider theoptimal debt ratio, investment, and dividend payment poli-cies for insurers with time-inconsistency. The asset can beinvested in a financial market which contains a risky assetand a risk-free asset. The objective is to maximize theexpected nonconstant discounted utility of dividend paymentuntil a determinate time. This is a time-inconsistent controlproblem.

The paper entitled “Strong Solutions and Global Attrac-tors for Kirchhoff Type Equation” by X. Chen studies thelong-time behavior of the Kirchhoff type equation with lineardamping and proves the existence of a strong solution andthe semigroup associated with the solution possesses a globalattractor in the higher phase space.

C. Guo and K. Zhang in the paper entitled “Dis-turbance Attenuation via Output Feedback for NonlinearTime-Delay Systems with InputMatching Uncertainty” studythe problem of output feedback disturbance attenuationfor a class of uncertain nonlinear systems with inputmatching uncertainty and unknown multiple time-varyingdelays, whose nonlinearities are bounded by unmeasuredstates multiplying unknown polynomial-of-output growthrate. By skillfully combining the extended state observer,dynamic gain technique, and Lyapunov-Krasovskii theorem,

6 Mathematical Problems in Engineering

a delay-independent output feedback controller can be devel-oped with only one dynamic gain to guarantee the bound-edness of closed-loop system states and the achievement ofglobal disturbance attenuation in the 𝐿

2-gain sense.

The paper by H. Wang and W.Y. Huang entitled “TheDynamic Properties of a Nonlinear Economic Model withExtreme Financial Frictions” investigates a generalized eco-nomic model with two kinds of agents (farmers and land-lords). Farmers produce grains by renting lands from land-lords. The economy is assumed to be with extreme frictionsso that there are no markets for agents to trade grains. Therental rate is determined by the equilibrium of the supplyand demand. The psychological anticipation is taken intoaccount in the setting of this model. By using the optimalcontrol theory, the dynamic properties of the rental rate andits influence to the endogenous volatility are analyzed.

The paper entitled “Global Output Feedback Stabilizationfor a Class of Nonlinear Cascade Systems” by C.-Y. Liuet al. focuses on the problem of global output feedbackstabilization for a class of nonlinear cascade systems withtime-varying output function. By using the double-domina-tion approach, an output feedback controller is developed toguarantee the global asymptotic stability of the closed-loopsystem. The novel control strategy successfully constructsa unified Lyapunov function, which is suitable for bothupper-triangular and lower-triangular systems.

Q.Wang et al. in the paper entitled “Consensus Control ofMultiagent Systems with High-Order Nonlinear InaccurateDynamics and Dynamically Switching Undirected Topolo-gies” investigate the consensus control of a class of high-ordernonlinearmultiagent systems, whose topology is dynamicallyswitching directed graph. The high-order nonlinear dynam-ics is transformed into the one-order dynamics by structuringa sliding mode plane. Two consensus control protocols of theone-order dynamics are designed by feedback linearization.Under these control protocols, it is proved that the consensusof new variable only requires a weaker topology condition.

The paper by J. Yogambigai et al. entitled “ExponentialLagrange Stability for Markovian Jump Uncertain NeuralNetworks with Leakage Delay and Mixed Time-VaryingDelays via Impulsive Control” studies the problem of expo-nential Lagrange stability analysis of Markovian jump neuralnetworks with leakage delay and mixed time-varying delays.By utilizing the Lyapunov functional method, employing thefree-weighting matrix approach and inequality techniques inmatrix form, the novel stability criteria are established suchthat the suggested neural network is exponentially stable inLagrange sense.

The paper entitled “Adaptive Tracking Control for a Classof Manipulator Systems with State Constraints and Stochas-tic Disturbances” by W. Sun et al. constructs an adaptivecontroller for a class of stochastic manipulator nonlinearsystems. A tan-type Barrier Lyapunov Function (BLF) isemployed to deal with state constraints. The proposed controlscheme guarantees the output error convergence to a smallneighborhood of zero. All the signals in the closed-loopsystem are bounded.

Z. Li et al. in the paper entitled “A Novel Fifth-Degree Strong Tracking Cubature Kalman Filter for

Two-Dimensional Maneuvering Target Tracking” presenta novel fifth-degree strong tracking cubature Kalmanfilter to improve the two-dimensional maneuvering targettracking accuracy. A new fifth-degree cubature rule is usedto approximate the intractable nonlinear Gaussian weightedintegral in the nonlinear Kalman filtering framework, and anovel fifth-degree cubature Kalman filter is proposed. Thesuboptimal fading factor is designed for the filter to adjust thefiltering gain matrix online and force the residual sequencesmutually orthogonal, thus improving the ability of the filterto track the mutation state, and the fifth-degree strongtracking cubature Kalman filter is derived. The suboptimalfading factor is calculated in a new method, which reducesthe number of calculations for the cubature points fromthree times to twice without calculating the Jacobian matrix.

Conflicts of Interest

The editors declare that they have no conflicts of interestregarding the publication of this special issue.

Acknowledgments

The guest editorial team would like to express gratitude toall the authors for their interest in selecting this specialissue as a venue for disseminating their scholarly work. Theeditors also wish to thank the anonymous reviewers for theircareful reading of the manuscripts submitted to this specialissue collection and their many insightful comments andsuggestions.

Xue-Jun XieJu H. Park

Hiroaki MukaidaniWeihai Zhang

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