Consensus control of multi-manipulator systems based on disturbance observer under Markov switching topologies

In this paper,to solve the consensus control problem of multi-manipulator systems under Markov switching topologies,we propose a distributed consensus control strategy based on disturbance observer.In multi-manipulator systems,external disturbance described by heterogeneous exogenous systems is considered,and all communication topologies are directed.First,a disturbance observer is presented to suppress the influence of unknown external disturbance,and the equivalent compensation is introduced into the control protocol in multi-manipulator systems.Then,a novel control protocol based on neighbor information is designed,which guarantees that multi-manipulator systems reach consensus under Markov switching topologies.Finally,two simulation examples verify the validity of the theoretical result.

Sampled-Data Stabilization of a Class of Stochastic Nonlinear Markov Switching System with Indistinguishable Modes Based on the Approximate Discrete-Time Models

This paper investigates the stabilization issue for a class of sampled-data nonlinear Markov switching system with indistinguishable modes.In order to handle indistinguishable modes,the authors reconstruct the original mode space by mode clustering method,forming a new merged Markov switching system.By specifying the difference between the Euler-Maruyama(EM)approximate discrete-time model of the merged system and the exact discrete-time model of the original Markov switching system,the authors prove that the sampled-data controller,designed for the merged system based on its EM approximation,can exponentially stabilize the original system in mean square sense.Finally,a numerical example is given to illustrate the effectiveness of the method.

An LMI-based variable structure control for a classof uncertain singular Markov switched systems

An H-infinifty variable structure control is presented for singular Markov switched systems with mismatched norm-bounded uncertainties and mismatched norm-bounded external disturbances. It is shown that the sliding mode dynamics on the given switching surface is regular, impulse-free, and stochastically stable and satisfies H-infinity performance. A variable structure controller is designed to guarantee that the system trajectory converges to the linear switching surface in some finite time. Finally, a numerical example is solved to show the effectiveness and validness of the theoretical results.

国际粮食价格运行规律的实证研究

本文运用四状态Markov-Switching模型,考察国际粮食价格的运行规律。根据该模型,国际粮食价格上涨率可分为四个阶段:紧缩阶段(平均上涨率-5.2941%)、恢复阶段(平均上涨率-1.3225%)、温和上涨阶段(平均上涨率0.9286%)与快速上涨阶段(平均上涨率5.2832%)。紧缩阶段是一个不稳定的阶段,且平均持续时间最短,只有1.65个月。快速上涨阶段也不稳定,平均持续时间为3.48个月。恢复阶段与温和上涨阶段是一个较为稳定的状态,平均持续时间较长,分别为7.35个月与6.83个月。国际粮食价格阶段的转移存在着"跳跃式"转移,国际粮食价格容易从紧缩阶段直接"跳跃"至快速上涨阶段,与此同时,也容易从快速上涨阶段直接下落至恢复阶段。另外,脉冲响应函数分析显示:相邻两状态的转移,其调整幅度较小,而两状态之间间隔越大,在转移过程中其调整幅度就越大。

货币政策对股市的非对称性影响实证研究——以逆回购为例

在中国的股票市场当中,政府所采取的货币政策变动带来的各种后果不仅能够显著影响股票市场的运行,而且还表现出许多与传统经济金融理论大不相同的现象,所以研究此手段对股票市场的特征影响,具有一定的理论和现实意义,由于逆回购是中国人民银行向市场注入流动性的主要手段,位列各类流动性工具之首。央行通过交替使用不同期限的逆回购,令资金投放更加精准。现在逆回购利率已成为市场新的利率风向标。所以文章选取逆回购为代表性货币政策,通过实证研究运用Markov Switching模型对市场进行简单划分,选取了2000~2019年的月度股票收益率,对我国股票市场进行模拟,将上海股票市场分为牛市与熊市两种市场状态,根据平滑概率推断出牛市出现次数较少,持续时间较短;熊市出现次数较多,持续时间较长。结论显示:逆回购对上海股票市场影响存在非对称效应,这种非对称性效应主要表现在逆回购在不同的市场行情中(不同的状态机制下)逆回购的发行量增速与逆回购利率缺口变动对股票市场的影响在显著水平下,作用方向、影响强度等方面存在差异。对牛市的影响小于对熊市的影响,最后基于理论与实践挖掘出内在的经济规律,从而对改善提升社会的经济发展完善货币政策建立机制等方面提出一些政策建议。

A regime-switching stochastic SIR epidemic model with a saturated incidence and limited medical resources

The stochastic switching SIR epidemic model with saturated incidence and limited medical treatment is investigated in this paper.By using Lyapunov methods and Ito formula,we first prove that the system has a unique global positive solution with any positive initial value.Then combining inequality technique and the ergodic property of Markov switching,the suficient conditions for extinction and persistence in the mean of the disease are established.The results demonstrate that increasing medical resources and improving supply efficiency can accelerate the transition from the persistent state to the extinct state.Meanwhile,the high incidence rate will slow down the extinction of the disease.Specially,the switching noise can induce the system to toggle between the extinct and persistent states.Finally,some numerical simulations are carried out to confirm the analytical results.

Load analyzing of nonstationary load history of engineering vehicles by switching Markov chain

Engineering vehicles are widely used under various harsh working conditions.For many components in them,service loadings they suffered are usually random and nonstationary due to their remarkable characteristic called cyclic operation.To deal with that,section method can be applied.However,this method will neglect those transition cycles caused by switching load section,which can contribute a lot to fatigue.In order to consider those transition cycles,this paper applied the model called“Switching Markov Chain of Turning Points”(SMCTP).Then the expected rain-flow matrix is compared with the overall rain-flow matrix conducted by section method.The comparison result shows that SMCTP can perform well in processing nonstationary loadings.As a result,the Switching Markov Chain method(SMC)was proved to be effective in stochastically characterizing the nonstationary switching loadings of engineering vehicles.

Finite-Time Stability and Stabilization of Discrete-Time Switching Markov Jump Linear System

Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems.Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided,and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities(LMIs).Finally,numerical examples are given to show the feasibility and effectiveness of the results.

A Markov Copula Model with Regime Switching and Its Application

Regime switching,which is described by a Markov chain,is introduced in a Markov copula model.We prove that the marginals（X,H^i）,i = 1,2,3 of the Markov copula model（X,H） are still Markov processes and have martingale property.In this proposed model,a pricing formula of credit default swap（CDS） with bilateral counterparty risk is derived.

Common Fixed Point Theorems and Q-property for Quasi-contractive Mappings under c-distance on TVS-valued Cone Metric Spaces without the Normality

In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stochastic pantograph equation and modulated by a continuous-time finite-state Markov chain. By virtue of classical variational approach, duality method, and convex analysis, we obtain a stochastic maximum principle for the optimal control.

STABILITY ANALYSIS OF THE SPLIT-STEP THETA METHOD FOR NONLINEAR REGIME-SWITCHING JUMP SYSTEMS

In this paper,we investigate the stability of the split-step theta(SST)method for a class of nonlinear regime-switching jump systems–neutral stochastic delay differential equations(NSDDEs)with Markov switching and jumps.As we know,there are few results on the stability of numerical solutions for NSDDEs with Markov switching and jumps.The purpose of this paper is to enrich conclusions in such respect.It first devotes to show that the trivial solution of the NSDDE with Markov switching and jumps is exponentially mean square stable and asymptotically mean square stable under some suitable conditions.If the drift coefficient also satisfies the linear growth condition,it then proves that the SST method applied to the NSDDE with Markov switching and jumps shares the same conclusions with the exact solution.Moreover,a numerical example is demonstrated to illustrate the obtained results.

Persistence and extinction of Markov switched stochastic Nicholson’s blowflies delayed differential equation

In this paper,we study the persistence and extinction of Markov switched stochastic Nicholson's blowflies delayed differential equation.We derive sufficient conditions of persistence and extinction for blowflies population,respectively,which solve one of open problems proposed by Zhu et al.

Ergodic stationary distribution of two stochastic tuberculosis models with imperfect vaccination and early and late latency

This contribution probes into ergodic stationary distribution for two stochastic SVELIT(susceptible-vaccinated-early latent-late latent-infective-treated)tuberculosis(TB)models to observe the impact of white noises and color noises on TB control in random environments.We first investigate the existence and uniqueness of ergodic stationary distribution(EUESD)for the autonomous SVELIT model subject to white noises via the proper Lyapunov functions,and suficient conditions on the extinction of disease are acquired.Next,sufficient conditions for the EUESD and the extinction of disease for the SVELIT model with Markov switching are also established.Eventually,some numerical examples validate the theoretical findings.What's more,it has been observed that higher amplitude noises may lead to the eradication of TB,which is conducive to TB control.

Refined analysis and prediction of natural gas consumption in China

In view of the abrupt and phased features of natural gas consumption,this paper attempts to predict natural gas consumption in China with a refined forecasting approach.First,we establish a Markov switching(MS)model to identify the phase characteristics after eliminating change points in the natural gas consumption sequence,using the product partition model(PPM).The results show that there are"rapid growth"and"slow growth"regimes in the development process of natural gas consumption in China.Second,the Bayesian model average(BMA)method is employed to determine the core determinants of natural gas consumption under sub-regimes,and it is determined that there are significant differences in the influencing factors under different regimes and periods.Third,this paper establishes the BMA model of the"rapid growth"regime after predicting the state of future natural gas consumption in China.We find that,compared to some other models,the BMA model that fully recognizes the regime without considering change points has the best predictive performance.Finally,the results of static and dynamic scenario analyses show that natural gas consumption continues to rise in 2019 and has obvious seasonal charac-teristics,while possible ultra-rapid growth of consumption in the future provides a new requirement for the supply of natural gas.

A stochastic switched SIRS epidemic model with nonlinear incidence and vaccination:Stationary distribution and extinction

In this paper,a stochastic epidemic system with both switching noise and white noise is proposed to research the dynamics of the diseases.Nonlinear incidence and vaccination strategies are also considered in the proposed model.By using the method of stochastic analysis,we point out the key parameters that determine the persistence and extinction of the diseases.Specifically,if R0^s is greater than 0,the stochastic system has a unique ergodic stationary distribution;while if R ^* is less than 0,the diseases will be extinct at an exponential rate.