High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.

Book Announcement of L. Celentano, Robust Tracking Controllers Design with Generic References for Continuous and Discrete Uncertain Linear SISO Systems, LAP LAMBERT Academic Publishing, 2012

In this book new results on controller design techniques for the tracking of generic reference inputs are presented. They allow the design of a controller for an uncertain process, either continuous or discrete-time, without zeros, and with measurable state. The controller guarantees that the control system is Type 1 and has the desired constant gain and poles or that the control system tracks, with a specified maximum error and with a specified maximum time constant, a generic reference with bounded derivative (variation in the discrete-time case), also in the presence of a generic disturbance with bounded derivative (variation). In addition, it is considered the case in which the reference is known a priori. The utility and the efficiency of the proposed methods are illustrated with attractive and significant examples of motion control and temperature control. This book is useful for the design of control systems, especially for manufacturing systems, that are versatile, fast, precise and robust.

A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems

In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.

STATIONARITY OF A CLASS OF LARGE-SCALE DISCRETE-TIME STOCHASTIC SYSTEMS

Stationarity of a class of stochastically interconnecteil discrete-timesystems is analyzed by utilizins results from ergodic theory of general stateMarkov chains, incorporated with the so called large-scale system approach.

MODELING AND PERFORMANCE ANALYSIS FOR THE SERIAL AND PARALLEL PRODUCTION SYSTEM BASED ON GSPN

Differed from the existed applications of generalized stochastic Petri net(GSPN) theory in machine-tool manufacturing system, reliability computation of FMS, testabilityparameters determination and fault analysis, a new idea of applying GSPN to model and performanceanalysis for the serial and parallel production system is proposed. And one typical discrete eventdynamic system (DEDS), turner-unit of palletizing system, is taken as a real case to research. Basedupon the established GSPN models, the working performances of serial and parallel layout arecompared. Furthermore, their differences of working mechanisms including feeding mechanism,coordinating mechanism and monitoring mechanism are discussed. Thus the theoretical basis which ishelpful to appraise layout plan and its reasonableness is provided. Meanwhile, the research resultsshow that parallel layout is more advantageous to greatly improve the operational speed ofproduction system than serial one.

Temporal Statistical Downscaling of Precipitation and Temperature Forecasts Using a Stochastic Weather Generator

Statistical downscaling is based on the fact that the large-scale climatic state and regional/local physiographic features control the regional climate. In the present paper, a stochastic weather generator is applied to seasonal precipitation and temperature forecasts produced by the International Research Institute for Climate and Society （IRI）. In conjunction with the GLM （generalized linear modeling） weather generator, a resampling scheme is used to translate the uncertainty in the seasonal forecasts （the IRI format only specifies probabilities for three categories： below normal, near normal, and above normal） into the corresponding uncertainty for the daily weather statistics. The method is able to generate potentially useful shifts in the probability distributions of seasonally aggregated precipitation and minimum and maximum temperature, as well as more meaningful daily weather statistics for crop yields, such as the number of dry days and the amount of precipitation on wet days. The approach is extended to the case of climate change scenarios, treating a hypothetical return to a previously observed drier regime in the Pampas.

Improved results on passivity analysis of discrete-time stochastic neural networks with time-varying delay

The problem of passivity analysis for a class of discrete-time stochastic neural networks (DSNNs) with time-varying interval delay was investigated. The delay-dependent sufficient criteria were derived in terms of linear matrix inequalities (LMIs). The results are shown to be generalization of some previous results and are less conservative than the existing works. Meanwhile, the computational complexity of the obtained stability conditions is reduced because less variables are involved. A numerical example is given to show the effectiveness and the benefits of the proposed method.

Delay-Dependent Robust H∞ Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

This paper considers the problem of delay-dependent robust optimal H∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H∞ noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H∞ controller which minimizes the H∞ noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

Robust Optimal H∞ Control for Uncertain 2-D Discrete State-Delayed Systems Described by the General Model

This paper investigates the problem of robust optimal H∞ control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H∞ state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H∞ noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.

含信号调制噪声和频率波动的时滞分数阶振子的随机共振

本文研究了含信号调制噪声和频率波动的小时滞线性分数阶振子的随机共振.利用分数阶Shapiro-Loginov公式和Laplace变换技巧,本文首先推导了系统响应的一阶稳态矩和稳态响应振幅增益(Output Amplitude Gain, OAG)的解析表达式,然后讨论了分数阶、时滞和噪声参数对OAG的影响.结果显示:各参数对OAG的影响均呈现非单调变化的特点,表明系统出现广义随机共振.特别地,分数阶与时滞的协同作用可能诱导随机共振的多样化.这就为在一定范围内调控随机共振提供了可能.

Infinite horizon indefinite stochastic linear quadratic control for discrete-time systems

This paper discusses discrete-time stochastic linear quadratic （LQ） problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefinite. The problem gives rise to a generalized algebraic Riccati equation （GARE） that involves equality and inequality constraints. The well-posedness of the indefinite LQ problem is shown to be equivalent to the feasibility of a linear matrix inequality （LMI）. Moreover, the existence of a stabilizing solution to the GARE is equivalent to the attainability of the LQ problem. All the optimal controls are obtained in terms of the solution to the GARE. Finally, we give an LMI -based approach to solve the GARE via a semidefinite programming.

Global synchronization of general delayed complex networks with stochastic disturbances

In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule and the linear matrix inequality （LMI） optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions.

A New Method of State Estimation for Singular Discrete-time Stochastic Linear System

Using theory of Bayesian Dynamic Models and Forecasting , this paper mainly deals with the problem on state estimation for singular discrete time stochastic linear system. And a new method of state estimation linear Bayes estimation (LBE for short) has been proposed.

Iterated Logarithm Laws on GLM Randomly Censored with Random Regressors and Incomplete Information

In this paper, we define the generalized linear models (GLM) based on the observed data with incomplete information and random censorship under the case that the regressors are stochastic. Under the given conditions, we obtain a law of iterated logarithm and a Chung type law of iterated logarithm for the maximum likelihood estimator (MLE) in the present model.

A New Approach to Optimal Filtering for SingularDiscrete-Time Stochastic Linear System

Based on the theory of Bayes forecasting, this paper mainly deals with the problem onthe state estimation for singular discrete-time stochastic linear system. And a new approach to optimalfiltering-linear Bayes estimation (LBE) has been proposed.

具有加性和乘性噪声的线性离散时间随机系统的无模型最优跟踪控制

本文研究一类同时受加性和乘性噪声影响的离散时间随机系统的最优跟踪控制问题.通过构造由原始系统和参考轨迹组成的增广系统,将随机线性二次跟踪控制(SLQT)的成本函数转化为与增广状态相关的二次型函数,由此推导出用于求解SLQT的贝尔曼方程和增广随机代数黎卡提方程(SARE),而后进一步针对系统和参考轨迹动力学信息完全未知的情形,提出一种Q-学习算法来在线求解增广SARE,证明了该算法的收敛性,并采用批处理最小二乘法(BLS)解决该在线无模型控制算法的实现问题.通过对单相电压源UPS逆变器的仿真,验证了所提出控制方案的有效性.

STOCHASTIC DIFFERENTIAL EQUATIONS AND STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEM WITH LEVY PROCESSES

在这篇论文，作者首先作为噪音来源与 L é vy 过程学习二种随机的微分方程(SDE ) 。基于这些 SDE 和 Lévy 进程驾驶的多维的向后的随机的微分方程( BSDE )的解决方案的存在和唯一，作者继续学习一随机线性二次( LQ )有 Lévy 进程的最佳的控制问题，在状态和控制的费用 weighting 矩阵被允许不定的地方。包含平等和不平等限制的一个种新随机的 Riccati 方程从方形的结束的想法被导出，它的解决之可能性被证明为 well-posedness 和能具有州的反馈或 LQ 问题的开环的形式的最佳的控制的存在足够。而且，作者获得一些特殊情况的 Riccati 方程的答案的存在和唯一。最后，二个例子被举说明这些理论结果。