Abstract:In recent years,wireless sensor networks with sensing,computation and communication abilities have had broad applications in a variety of engineering practice,production process,and daily life.In addition,with rapid progress of micro-electronics and digital signal technologies,discrete digital controllers/filters have been widely used,which has led to the sampled-data issues.To reflect the state-of-the-art of the advances in this emerging area,this paper provides a survey on distributed sampled-data filtering for sensor networks.First,the current progress on distributing filtering methods over sensor networks is reviewed.Then,the study on the control/filtering problems of sampled-data systems based on different sampling schemes is summarized in detail.Subsequently,most recent results on sampled-data distributed filtering problems over sensor networks are highlighted.Finally,a coherent framework on possible research topics is established on the distributed filtering for sensor networks with sampled-data.

Abstract:In recent years,singular stochastic systems governed by the Itô stochastic differential equation have received much attention due to their extensive applications to some practical areas.However,it is very complicated to discuss singular stochastic systems since the system equation includes both the singular matrix and the diffusion matrix simultaneously.In this paper,research development of several important and basic problems for singular Itô stochastic systems are concluded,including mainly the existence condition for the solution to the system equation,the general Itô formula,the definition of admissibility and the issue of stability.Also,some research perspectives are given for results of different references.Finally,some prospects to the unresolved problems are presented.

Abstract:This paper reviews the current developments in the study of hybrid stochastic differential delay equations (SDDEs) with emphasis on the existence-and-uniqueness theorems,boundedness,stability and stabilization.

Abstract:This paper provides an overview of recent advances of theory on stochastic stabilization and destabilization.The paper reviews a general theory on stochastic stabilization and destabilization of continuous-time systems and then illustrates the developments of theory on stabilization by noise with the applications and generalizations of this theory from four aspects.Moreover,this paper reviews some recent development of stochastic stabilization for discrete-time systems.

Abstract:From aspects of the research methods,this paper reviews various classes of stability results of continuous stochastic systems,and discusses the relationship among these stabilities under different conditions.

Abstract:In this paper,a survey is given for the investigation on the stability of numerical schemes of stochastic differential equations in the past years.As a related topic,the convergence of the schemes is involved.The paper introduces the achieved results by literatures for the classical Itô stochastic differential equations,stochastic functional differential equations of the neutral type,and the stochastic differential equations with Markov or Poisson jumps.The involved numerical schemes include the Euler-Maruyama scheme,the Backward Euler-Maruyama scheme,the θ scheme,and the split-step scheme,etc.The paper analyzes the academic thoughts in some classical literatures on the stability equivalence theorems and proposes some problems and challenges for further investigations on the numerical computations and simulations of stochastic differential equations at the end of the paper.

Abstract:Recently,the artificial intelligence (AI),especially with the deep learning techniques,has achieved great success in various applications.This paper gives an overview on the artificial intelligence,including aspects of its commercialized development,the many tribes of AI with origin and history,successful stories based on deep learning,as well as the remaining challenges and possible development trends in future.

Abstract:The backward stochastic differential equation theory has been developed and improved in recent years,and then it is widely used in mathematical finance.Meanwhile,the stochastic control has become an important method to study the portfolio risk management problem.In this paper,we focus on how to study option pricing,mean-variance and expected utility maximization problems by using the stochastic control method with incomplete information.

Abstract:With the development of stochastic nonlinear control,more and more researchers have paid attention to the control of stochastic nonholonomic systems.Firstly,we give the results of stabilization for stochastic nonholonomic systems,which contain state feedback stabilization,output feedback stabilization and stabilization of mobile robots.Secondly,the tracking problems of stochastic nonholonomic systems are introduced.In the end,we analyze the prospect of the control for stochastic nonholonomic systems and give six future research challenges based on above summary.

Abstract:This paper gives a summary of recent work on set-valued systems.On the identification side,for different model structures,different system noises and different set cases,some effective methods such as parameter decoupling,full rank input design,joint identifiability,empirical measure method without truncation and recursive projection identification algorithm are introduced.Based on these methods,the results show that the accurate estimates of the parameters can be achieved even under set-valued information.On the adaptive control side,the asymptotically optimal adaptive control is designed for a class of gain systems with set-valued observations.On the consensus control side,the two-time scale consensus control and the recursive projection consensus control are designed.The multi-agent systems can achieve consensus control by any of the two consensus algorithms.On the application side,we apply set-valued identification methods to complex disease modeling and radar target recognition problems.A new and more effective statistical verification method is constructed.The recognition rate is improved by 10% under low signal-noise ratio.

Abstract:Focused on Cohen-Grossberg neural networks,this paper investigates the mean-square exponential stability by means of the vector Lyapunov function.This method ensures that the impulsive stochastic Cohen-Grossberg neural network is exponentially stable.Finally,an example is used to illustrate the conclusions.

Abstract:In this paper,we explain the valuation issue of private equity investment.First,we briefly introduce the development history and research results of the portfolio problem.Then we discuss the research situation of the valuation issue of private equity investment in detail,including the portfolio selection of limited partners,as well as the research on the value evaluation system and evaluation methods of investment enterprises.And we give the model to be studied,namely the private equity model with unspanned risk.Finally,we give the expansion of the framework of the model under inflation,Knightian uncertainty and jump diffusion environment.