H∞ control of networked control systems based on Markov jump unified model

This paper focuses on a new H_∞ controller design issue for networked control systems with external disturbance as well as random time delays and packet dropouts in forward and feedback channels, which are modeled by multiple Markov chains in a unified style. The output feedback controller is designed to stabilize the networked control system and also achieves the prescribed H_∞ disturbance attenuation level. The addressed controller design problem is transformed into a nonlinear minimization problem with LMI constraints. An illustrative example is provided to show the effectiveness of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.     

具有噪声约束的 时滞Markov跳变网络给定时间一致性协议设计

本文研究网络连接系统在随机Markov跳变拓扑结构,通信时滞,外部干扰等情形下的给定时间一致性协议设计方法.基于有限短时间理论,放宽对系统不一致状态渐近收敛于零的要求,在预先给定的时间区域内,设法使网络中各子系统的不一致状态在期望范围内受限运动,从而提出给定时间一致性定义,并进一步设计给定时间一致性控制算法.不仅从时间角度为降低渐近一致的工程保守性提供了思路,且所提的模型转换新方法使得设计的控制协议更具通用性.仿真结果验证了所提算法的有效性.     

基于有限频段的Markov跳变系统有限时间H∞滤波

传统Markov跳变系统H∞滤波方法要求所有子系统对全频域的噪声具有同样的干扰抑制水平,由于没有充分利用噪声的频率信息,导致传统滤波方法可能含有较大的保守性.本文针对特定频段的干扰信号,提出基于有限短时间的H∞滤波器设计方法.在引入有限频段的同时,结合有限短时间稳定理论,提出有限频段以及有限时间两尺度滤波方案,为降低滤波理论的工程保守性提供了思路.仿真结果表明本文所提滤波方法与现有滤波方法相比,具有一定的优越性.     

Asynchronous H∞ filtering of continuous‐time Markov jump systems

The paper investigates the asynchronous H_∞ filtering design problem for continuous‐time linear systems with Markov jump. The hidden Markov jump principle is applied to represent the asynchronous situation between the target system and the designed filter. Via a Lyapunov technique, two sufficient conditions are developed to guarantee that the filtering error system is stochastically stable with a prescribed H_∞ noise attenuation level. Furthermore, three filtering design approaches are developed in the form of linear matrix inequalities. Finally, one example is provided to show the effectiveness and feasibility of the developed methods.     

A Markovian jump system approach to consensus of heterogeneous multiagent systems with partially unknown and uncertain attack strategies

The problem of robust leader‐following consensus of heterogeneous multiagent systems subject to deny‐of‐service attacks is investigated, where attack strategies are partially unknown and uncertain to defender. A Markovian jump system approach is proposed, that is, capable of describing the occurrence of different attack strategies, and the occurring probability of each attack strategy is represented by the transition probability of the Markovian jump model. Then, sufficient conditions are derived such that the output tracking performance can be guaranteed. In order to design the controller gains, some slack matrices are introduced, which can provide some design freedom. Finally, it is shown that the controller design results can be applied to the multivehicle position‐tracking system. The simulation results reveal that the consensus performance is much better if one has more statistics information on attacks.     

Robust H∞ control of Markovian jump systems with uncertain switching probabilities

This paper is concerned with the robust H_∞ control problem for a class of Markovian jump systems with uncertain switching probabilities, whose uncertainties are assumed to be elementwise bounded. First, new criterion of H_∞ performance for such uncertain systems is given. Then, new sufficient condition for H_∞ controller is established as strict linear matrix inequalities. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

H∞ control for uncertain one‐sided Lipschitz nonlinear systems in finite frequency domain

The current article discusses the H_∞ disturbance attenuation control design problem for one‐sided Lipschitz systems in finite frequency domain. Models containing norm‐bounded parameter uncertainties, disturbances, and input nonlinearities are considered. By contrast to existing full frequency methods, the H_∞ controller is computed depending on the frequency ranges of disturbances. The finite frequency disturbance attenuation index is initially defined. Thanks to Finsler's lemma, sufficient and less conservative analysis conditions are also derived for the closed‐loop system. Then, synthesis conditions in the low, middle, and high frequency ranges as well as the whole frequency range, are formulated in terms of linear matrix inequalities. At last, to prove the effectiveness and the superiority of the proposed approach, a physical example is used and a comparative study is done.     

Finite‐Time H∞ Filtering for Nonlinear Continuous‐Time Singular Semi‐Markov Jump Systems

The stochastic finite‐time H_∞ filtering issue for a class of nonlinear continuous‐time singular semi‐Markov jump systems is discussed in this paper. Firstly, sufficient conditions on singular stochastic H_∞ finite‐time boundedness for the filtering error system are established. The existence of a unique solution for the corresponding system is also ensured. Secondly, based on the bounds of the time‐varying transition rate, without imposing constraints on slack variables, a novel approach to finite‐time H_∞ filter design is proposed in the forms of strict LMIs, which guarantees the filtering error system is singular stochastic H_∞ finite‐time bounded and of a unique solution. Compared with the existing ones, the presented results reveal less conservativeness. Finally, one numerical example is exploited to testify the advantage of the proposed design technique.     

随机时滞马尔可夫跳跃系统的比例-积分跟踪控制

针对具有时变时滞和未知非线性的随机马尔可夫跳变系统,基于传统的PI控制策略和线性矩阵不等式算法,提出一种具有随机稳定性能、跟踪性能和鲁棒性能的多目标控制器设计方案.运用Lyapunov稳定性理论并引入L<,1>性能指标,构造出具有PI结构的跟踪控制器,保证了随机马尔可大跳跃系统的稳定性和跟踪性能,实现了系统跟踪性能的优...     

Observer‐based H ∞ control on nonhomogeneous Markov jump systems with nonlinear input

This paper considers the problem of observer‐based H _∞ controller design for a class of discrete‐time nonhomogeneous Markov jump systems with nonlinear input. Actuator saturation is considered to be a nonlinear input of such system and the time‐varying transition probability matrix in the system is described as a polytope set. Furthermore, a mode‐dependent and parameter‐dependent Lyapunov function is investigated, and a sufficient condition is derived to design observer‐based controllers such that the resulting error dynamical system is stochastically stable and a prescribed H _∞ performance is achieved. Finally, estimation of attraction domain of such nonhomogeneous Markov jump systems is also made. A simulation example shows the effectiveness of developed techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

Event‐triggered control for networked Markovian jump systems

The problem of H_∞ control for networked Markovian jump system under event‐triggered scheme is studied in this paper. In order to reduce the utilization of limited network bandwidth, a dynamic discrete event‐triggered scheme to choose the transmitted data is designed. A Markovian jump time‐delay system model is employed to describe the event‐triggered scheme and the network related behavior, such as transmission delay, data package dropout, and disorder. Furthermore, a sufficient condition is derived to guarantee that the resulting closed‐loop system is stable and has a prescribed performance index. A co‐design method for the H_∞ controller and the event‐triggered scheme is then proposed. The effectiveness and potential of the theoretic results obtained are illustrated by a simulation example. Copyright © 2014 John Wiley & Sons, Ltd.     

Derandomisation-based multiple frequency control for stochastic Markov jump systems

Under the framework of derandomisation approach, the state feedback control issues for both continuous-time and discrete-time Markov jump linear systems (MJLSs) are investigated to meet multiple performance objectives over multiple frequency ranges. Because of the stochastic jumping among different modes, the generalised Kalman–Yakubovic–Popov lemma-based finite-frequency controller design approach cannot be directly applied to MJLSs. To overcome this limitation, a derandomisation approach is established by transforming the original stochastic multiple modes systems to deterministic ones. Then the multiple frequency controllers for both discrete-time and continuous-time MJLSs are designed to guarantee the multiple performances of the closed-loop systems. To verify the effectiveness of the developed algorithms, examples are presented, where the performance requirements include specifications in low-frequency and high-frequency ranges, respectively.     

Time‐varying filter design for semi‐Markov jump linear systems with intermittent transmission

This paper focuses on the filter design problem for semi‐Markov jump linear systems. The system outputs are transmitted to the filter via networks, and it is assumed that the transmission is imperfect with data packet dropouts subject to the Bernoulli random binary distribution. A σ‐error mean square stability criterion is first derived for the underlying systems. On the basis of the criterion, the H_∞ performance analysis is conducted. By constructing a time‐varying Lyapunov function, a time‐varying H_∞ filter scheme is investigated. Because the presented approach can cover the mode‐dependent and mode‐independent time‐invariant H_∞ filter schemes as special cases, the conservatism of the derived results is less than those of the time‐invariant filter schemes. An active suspension system with activator uncertainties is lastly presented to illustrate the effectiveness and feasibility of the derived theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

A finite frequency domain approach to fault detection observer design for linear continuous‐time systems

This paper deals with the fault detection observer design problem in finite frequency domain for linear time‐invariant continuous‐time systems with bounded disturbances. Two finite frequency performance indexes are introduced to measure the fault sensitivity and the disturbance robustness. Faults are considered in the low frequency domain while disturbances are considered in certain finite frequency domain. With the aid of the Generalized Kalman‐Yakubovich‐Popov lemma, the design methods are presented in terms of solutions to a set of linear matrix inequalities. An example of the VTOL aircraft is studied to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Distributed reliable H∞ consensus control for a class of multi‐agent systems under switching networks: A topology‐based average dwell time approach

This paper investigates the problem of distributed reliable H_∞ consensus control for high‐order networked agent systems with actuator faults and switching undirected topologies. The Lipschitz nonlinearities, several types of actuator faults, and exogenous disturbances are considered in subsystems. Suppose the communication network of the multi‐agent systems may switch among finite connected graphs. By utilizing the relative state information of neighbors, a new distributed adaptive reliable consensus protocol is presented for actuator failure compensations in individual nodes. Note that the Lyapunov function for error systems may not decrease as the communication network is time‐varying; as a result, the existing distributed adaptive control technique cannot be applied directly. To overcome this difficulty, the topology‐based average dwell time approach is introduced to deal with switching jumps. By applying topology‐based average dwell time approach and Lyapunov theory, the distributed controller design condition is given in terms of LMIs. It is shown that the proposed scheme can guarantee that the reliable H_∞ consensus problem is solvable in the presence actuator faults and external disturbance. Finally, two numerical examples are given the effectiveness of the proposed theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Fault Detection for Discrete‐Time Uncertain Systems with Polytopic Uncertainties: A Markov Approach

In this paper, the fault detection problem for a class of discrete‐time polytopic uncertain systems is studied. Different from the traditional methods dealing with polytopic uncertainties, not only its values but also the probability distributions are considered. First of all, the above process about polytopic uncertainty is described by applying a Markov process. Then, the original system with polytopic uncertainties becomes to be a Markovian jump system (MJS) without any uncertainty. Accordingly, the fault detection problem is transformed to be a similar one but considered for an MJS. Particularly, the fault detection and isolation (FDI) filter is constructed to be mode‐dependent and also said to be polytope‐dependent. Since more information of uncertainty is considered, it is claimed that the obtained results are less conservative. Finally, a practical example is used to show the effectiveness and superiority of the proposed methods.     

H ∞ control for discrete‐time nonlinear Markov jump systems with multiplicative noise and sector constraint

This paper addresses the finite horizon H _∞ control problem for a class of discrete‐time nonlinear Markov jump systems with multiplicative noise and nonlinear feedback device. The system nonlinearity occurs in a random way specified by a Bernoulli process, whereas the actuator and sensor nonlinearities are restricted to a sector region. Both the state and the dynamic output feedback H _∞ controllers are devised in terms of difference LMIs. The proposed approach not only allows the resulting system to achieve a prescribed disturbance attenuation level, but also enables the output of actuator/sensor to meet the designated sector condition. Moreover, it is also shown that our approach is well‐adapted for dealing with the discrete‐time Markov jump systems with saturated actuator and sensor. Finally, a backward iterative algorithm is provided to solve the obtained difference LMIs and a numerical example is presented to verify the efficiency of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Delay distribution based robust H∞ control of networked control systems with uncertainties

Network induced delay in networked control systems (NCS) is inherently non‐uniformly distributed and behaves with multifractal nature. However, such network characteristics have not been well considered in NCS analysis and synthesis. Making use of the information of the statistical distribution of NCS network induced delay, a delay distribution based stochastic model is adopted to link Quality‐of‐Control and network Quality‐of‐Service for NCS with uncertainties. From this model together with a tighter bounding technology for cross terms, H_∞ NCS analysis is carried out with significantly improved stability results. Furthermore, a memoryless H_∞ controller is designed to stabilize the NCS and to achieve the prescribed disturbance attenuation level. Numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

随机马尔可夫跳变系统的变结构控制设计

采用滑动扇区方法,研究了不确定随机马尔可夫跳变系统的变结构控制设计问题。首先给出随机马尔可夫跳变系统滑动扇区的定义,然后基于线性矩阵不等式技术,提出一种滑动扇区及变结构控制律设计方法。经过理论证明该控制律能够确保随机马尔可夫跳变不确定系统二次稳定,并有效地抑制抖振。最后数值仿真算例验证了控制方案的有效性。     

Delay‐range‐dependent H∞ control for Markovian jump systems with mode‐dependent time delays

This paper considers mean‐square exponential stability and H_∞ control problems for Markovian jump systems (MJSs) with time delays which are time‐varying in an interval and depend on system mode. By exploiting a novel Lyapunov‐Krasovskii functional which takes into account the range of delay, and by making use of some techniques, new delay‐range‐dependent stability result and bounded real lemma for MJSs are obtained, where the introduction of the lower bound of delay is shown to be advantageous for reducing conservatism. Moreover, a sufficient condition for the solvability of the H_∞ control problem is derived in terms of linear matrix inequalities. Finally, illustrative examples are presented to show the advantage and effectiveness of the proposed approaches. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society