Consensus in multi-agent systems with random delays governed by a Markov chain

This paper investigates the consensus problem in a multi-agent system with random delays governed by a Markov chain. The communication topology is assumed to be directed and fixed. With first-order dynamics under the sampled-data setting, we first convert the original system into a reduced-order one featuring the error dynamics. Accordingly, the consensus problem is transformed into the stabilization of the error dynamic system. Thereafter, based on the theory in stochastic stability for time-delay systems, a sufficient condition is established in terms of a set of linear matrix inequalities (LMIs). The mean square stability of the error dynamics is shown to guarantee consensus of the multi-agent system. By explicitly incorporating the transition probability of the random delay into consideration, the conservativeness in control design is reduced. A delay-dependent switching control scheme is developed by redesigning the adjacency matrix. Finally, simulation results are provided to verify the effectiveness of the proposed approach.     

鲁棒H∞滤波在随机风力发电系统中的应用

针对风力发电的随机系统模型设计鲁棒H∞滤波器,以减少扰动对系统误差影响,增强系统的鲁棒性。主要是利用李雅普诺夫稳定性理论推导出使随机不确定风力发电系统渐近稳定且鲁棒H∞滤波器存在的充分条件,将其表达成线性矩阵不等式(组),再利用Schur补引理将其转化成可求解的形式,并运用标准数值仿真软件进行求解。通过系统仿真得出扰动抑制度为γ=0.1150,结果表明所提出的滤波器设计方法对随机不确定风力发电系统更有效可行。     

PI tracking control for nonlinear time-varying delay Markov jump systems

This paper considers robust stochastic stability and PI tracking control problem for Markov jump systems with both input delay and an unknown nonlinear function. Based on the traditional PI control strategy, a new controller design scheme is proposed for nonlinear time-delay Markov jump systems which can realize multiple control objectives including robust stochastic stability and tracking performance. By using the Lyapunov stability theory and LMI algorithms, a sufficient condition for the solution to robust stochastic stability and tracking control problem is obtained. Then, the desired controller with PI structure is designed, which ensures the resulting closed-loop system is robust stochastically stable and the system state has favorable tracking performance. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.     

具有双边随机时延和丢包的网络控制系统稳定性分析

针对具有双边随机网络时延和丢包的网络控制系统,首先基于Markov的随机过程描述系统丢包的特性;然后利用系统增广矩阵的方法建立参数不确定的离散时间跳变系统模型,在考虑Markov链转移概率矩阵中部分元素未知甚至完全未知的条件下,采用Lyapunov稳定理论和随机理论的分析方法,设计依赖于丢包特性且满足系统均方稳定要求的时变控制器;最后通过数值算例仿真表明所提出方法的有效性.     

Minimum energy storage for power system with high wind power penetration using p-efficient point theory

Minimum energy storage （ES） and spinning reserve （SR） for day-ahead power system scheduling with high wind power penetration is significant for system operations. A chance-constrained energy storage optimization model based on unit commitment and considering the stochastic nature of both the wind power and load demand is proposed. To solve this proposed chance-constrained model, it is first converted into a deterministic-constrained model using p-efficient point theory. A single stochastic net load variable is developed to represent the stochastic characteristics of both the wind power and load demand for convenient use with the p-efficient point theory. A probability distribution function for netload forecast error is obtained via the Kernel estimation method. The proposed model is applied to a wind-thermal-storage combined power system. A set of extreme scenarios is chosen to validate the effectiveness of the proposed model and method. The results indicate that the scheduled energy storage can effectively compensate for the net load forecast error, and the increasing wind power penetration does not necessarily require a linear increase in energy storage.     

Simultaneous Fault Detection and Control for Markovian Jump Systems with General Uncertain Transition Rates

This paper investigates the simultaneous control and fault detection of Markovian jump systems with general transition rates allowed to be unknown and known with uncertainties. By introducing slack matrices, a new approach is developed to conquer the nonlinearity induced by unknown and uncertain transition rates. Then, sufficient conditions are presented to ensure the stochastic stability of the resultant closed-loop system and meet the robust and detection performance indices. Finally, an example is given to illustrate the effectiveness of the proposed theoretical results.     

基于切换频度的马尔科夫网络控制系统均方指数镇定

针对一类马尔科夫网络控制系统(Networked control system, NCS),研究了其均方指数镇定问题. 首先将网络控制系统建模为离散时间切换系统,子系统间的切换过程由一个转移概率矩阵已知的马尔科夫链描述, 并给出了子系统间切换频度的范围;进而基于随机过程理论和切换系统稳定性理论, 利用状态反馈实现了网络控制系统均方指数镇定,状态反馈控制律可通过求解一组线性矩阵不等式获得. 最后通过数值仿真例子验证了本文方法的有效性.     

一类脉冲随机混杂系统的鲁棒H无穷控制

本文研究具有外在扰动的脉冲Markov切换线性随机系统的鲁棒H无穷控制问题,分别从系统的鲁棒稳定性及鲁棒性能两方面进行分析,首先,利用多Lyapunov函数法对系统的稳定性进行分析,给出了系统鲁棒依概率稳定的充分条件,进一步,运用线性矩阵不等式(LMI)法对系统的鲁棒性能进行分析,给出相应的状态反馈增益矩阵和脉冲控制增益矩阵的求解方法,在此基础上得出了一个鲁棒H无穷控制律,并提出了一套基于Matlab软件的鲁棒控制器的设计方法。最后,数值算例说明所设计方法的有效性。     

转移概率部分未知的随机Markov 跳跃系统的镇定控制

研究一类随机Markov跳跃系统的稳定性与镇定控制问题.此类系统跳跃过程的转移概率部分未知,包括转移概率完全已知和完全未知两种情形,因而更具一般性.首先,给出保证随机Markov跳跃系统均方渐近稳定的充分性判据,并设计了相应的状态反馈镇定控制器;然后,基于矩阵的奇异值分解给出了系统静态输出反馈镇定控制器的设计方法,并将其归结为求解一组线性矩阵不等式（LMIs）的可行性问题;最后,通过数值仿真验证了所得结论的正确性.     

具有测量数据丢失的离散不确定时滞系统鲁棒Kalman滤波

研究了具有测量数据丢失的离散不确定时滞系统鲁棒Kalman滤波问题, 其中时延存在于系统状态和观测值中. 模型的不确定性通过在系统矩阵中引入随机参数扰动来表示, 测量数据丢失现象则通过一个满足Bernoulli分布且统计特性已知的随机变量来描述. 基于最小方差估计准则, 利用射影性质和递归射影公式得到一个新的滤波器设计方法, 并且保证了滤波器的维数与原系统相等. 与传统的状态增广方法相比, 当时延比较大时, 该方法可以有效降低计算量. 最后, 给出一个仿真例子说明所提方法的有效性.     

Sliding mode control for Markov jump linear uncertain systems with partly unknown transition rates

In this paper, based on sliding mode control approach, the robust stabilisation problem for a class of continuous-time Markovian jump linear uncertain systems with partly unknown transition rates is investigated. The transition rate matrix under consideration covers completely known, boundary known and completely unknown elements. By making use of linear matrix inequalities technique, sufficient conditions are presented to derive the linear switching surface and guarantee the stochastic stability of sliding mode dynamics. Then a sliding mode control law is designed to drive the state trajectory of the closed-loop system to the specified linear switching surface in finite time in spite of the existing uncertainties and unknown transition rates. Finally, an example is given to verify the validity of the theoretical results.     

Robust H ∞ control of discrete‐time Markovian jump systems in the presence of incomplete knowledge of transition probabilities and saturating actuator

This paper deals with the problem of robust H _∞ control for a class of discrete‐time Markovian jump systems subject to both actuator saturation and incomplete knowledge of transition probability. Different from the previous results where the transition probability is completely known, a more general situation where only partial information on the exact values of elements in transition probability matrix is considered. By introducing some free parameters to express the relationship for the known and the unknown elements of transition probability matrix in stability analysis, a criterion is established to guarantee the stochastic stability of the closed‐loop system as well as an H _∞ performance index. The concept of domain of attraction in mean square sense is used to analyze the closed‐loop stability, and the mode‐dependent H _∞ state‐feedback controller is designed. It is shown that, even in the absence of actuator saturation, the obtained result is less conservative than the existing one. A numerical example is provided to illustrate the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

无线接入网中一类联合调度算法的鲁棒稳定性分析

针对无线通讯中的随机时延抖动和外界干扰等会引发数据包传输的不稳定问题,研究不稳定传输下无线接入网中一类联合调度算法的鲁棒稳定性.首先,通过将基站中的队列尺寸定义为系统状态,并将不稳定传输建模为分布函数未知的随机扰动,利用具有一个弹性壁的Markov随机游走模型描述系统状态的变化;其次,根据在联合调度算法下系统状态的期望逗留时间等信息,得到该Markov模型的状态转移概率矩阵;再次,给出模型中状态正常返的充分条件,即队列尺寸的鲁棒稳定性判据,并对该判据进行验证;最后,通过数值仿真结果表明了所提方法的有效性.     

具有数据包丢失及转移概率部分未知的网络控制系统H∞控制

研究一类具有数据包丢失及状态转移概率部分未知的网络控制系统随机稳定性及H∞控制问题．传感器与控制器之间、控制器与执行器之间存在数据包丢失的网络控制系统被建模成具有4个子系统的跳变系统,4个子系统之间的跳变遵行Markov跳变过程,并具有部分未知的跳变概率．利用Lyapunov稳定性定理及线性矩阵不等式的求解方法得到该类系统随机稳定的充分条件,并给出了相应的∞状态反馈控制器的设计方法．数值仿真结果验证了本文方法的正确性和有效性．     

Robust exponential stability of uncertain stochastic systems with probabilistic time‐varying delays

This paper is concerned with the problem of delay‐distribution–dependent robust exponential stability for uncertain stochastic systems with probabilistic time‐varying delays. Firstly, inspired by a class of networked systems with quantization and packet losses, we study the stabilization problem for a class of network‐based uncertain stochastic systems with probabilistic time‐varying delays. Secondly, an equivalent model of the resulting closed‐loop network‐based uncertain stochastic system is constructed. Different from the previous works, the proposed equivalent system model enables the controller design of the network‐based uncertain stochastic systems to enjoy the advantage of probability distribution characteristic of packet losses. Thirdly, by applying the Lyapunov‐Krasovskii functional approach and the stochastic stability theory, delay‐distribution–dependent robust exponential mean‐square stability criteria are derived, and the sufficient conditions for the design of the delay‐distribution–dependent controller are then proposed to guarantee the stability of the resulting system. Finally, a case study is given to show the effectiveness of the results derived. Moreover, the allowable upper bound of consecutive packet losses will be larger in the case that the probability distribution characteristic of packet losses is taken into consideration.     

A multi-model adaptive predictor for stochastic processes with Markov switching parameters

This paper is concerned with prediction for discrete-time stochastic processes with switching parameters modelled as a finite-state Markov chain, whose transition probability matrix is assumed to be known. For these processes an adaptive predictor, called the multi-model adaptive predictor, is proposed. A simulation example shows the behaviour of the predictor.     

Boundary control of stochastic reaction‐diffusion systems with Markovian switching

This article focuses on the boundary control of stochastic Markovian reaction‐diffusion systems (SMRDSs). Both the cases of completely known and partially unknown transition probabilities are taken into account. By using the Lyapunov functional method, a sufficient condition is obtained under the designed boundary controllers to guarantee the asymptotic mean square stability for SMRDSs with completely known transition probabilities. For the case of partially unknown transition probabilities, we introduce free‐connection weighting matrices to handle the boundary control problem. When external disturbance enters the system, a sufficient criterion of H‐infinity boundary control is developed. Furthermore, robust stabilization is investigated for parametric uncertain SMRDSs in both cases. Two examples are presented to demonstrate the efficiency of the proposed approaches.     

Robust Stability of a Class of Uncertain Markov Jump Nonlinear Systems

This note addresses the problem of robust stability analysis for a class of Markov jump nonlinear systems subject to polytopic-type parameter uncertainty. A condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed. An estimate of a robust domain of attraction of the origin is also provided. The approach is based on a stochastic Lyapunov function with polynomial dependence on the system state and uncertain parameters. A numerical example illustrates the proposed result     

Stochastic stability and robust stabilization of semi‐Markov jump linear systems

The semi‐Markov jump linear system (S‐MJLS) is more general than the Markov jump linear system (MJLS) in modeling some practical systems. Unlike the constant transition rates in the MJLS, the transition rates of the S‐MJLS are time varying. This paper focuses on the robust stochastic stability condition and the robust control design problem for the S‐MJLS with norm‐bounded uncertainties. The infinitesimal generator for the constructed Lyapunov function is first derived. Numerically solvable sufficient conditions for the stochastic stability of S‐MJLSs are then established in terms of linear matrix inequalities. To reduce the conservativeness of the stability conditions, we propose to incorporate the upper and lower bounds of the transition rate and meanwhile apply a new partition scheme. The robust state feedback controller is accordingly developed. Simulation studies and comparisons demonstrate the effectiveness and advantages of the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.     

A singular system approach to robust sliding mode control for uncertain Markov jump systems

The robust sliding mode control for Markov jump systems with parameter uncertainties and an unknown nonlinear function is discussed. Based on a singular system approach and linear matrix inequality (LMI), a sufficient condition which guarantees the existence of linear switching surface and the stochastic stability of sliding mode dynamics is given. A sliding mode controller is designed such that the closed-loop system is convergent to the switching surface in finite time. A numerical example is given to show the effectiveness of the proposed method.