Markov跳变系统的有限时间状态反馈镇定

讨论一类含有限能量未知扰动的线性Markov跳变系统的有限时间镇定问题.针对连续系统和离散系统两种情况,利用构造的Lyapunov-Krasovskii函数,并结合线性矩阵不等式方法,分别证明并给出了跳变系统有限时间镇定控制器有解的充分条件.采用该方法设计的镇定控制器可使连续系统和离散系统对所有满足条件的未知扰动是有限时问有界和有限时间镇定的.最后通过数值示例表明了该设计方法的有效性.     

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.     

时滞执行器饱和Markov跳变系统的有限时间镇定

讨论了含执行器饱和的离散时滞Markov跳变系统在未知但有界扰动的情况下,针对系统模态转移概率部分未知的系统进行有限时间镇定的分析和研究。利用构造的Lyapunov函数和饱和非线性处理技术,对具有执行器饱和的离散时滞Markov系统进行研究,并提出了系统状态有限时间镇定的充分条件,结合线性矩阵不等式的方法,设计并实现了有限时间镇定状态反馈控制器。通过数值仿真,示例验证了该设计方法的有效性及潜在的应用性。     

马尔可夫跳变系统基于观测器的有限时间容错控制

针对具有一般不确定转移速率的单边Lipschitz Markovian跳变系统,设计了有限时间故障估计观测器和容错控制器.首先,提出一种自适应的有限时间故障估计观测器,它对未知输入具有鲁棒性,能够同时估计出系统的状态、执行器故障和传感器故障,并确保了误差系统的H_∞有限时间有界.然后,基于所估计的状态和执行器故障,提出一种有限时间故障容错控制方法确保闭环系统H_∞有限时间有界.通过线性矩阵不等式的形式,给出了所设计的有限时间观测器和控制器存在的充分条件.最后,通过一个仿真实例,验证了所提方法的有效性.     

基于有限时间输出反馈的线性扩张状态观测器

为快速、准确地观测系统中的未知扰动及状态, 提出一种有限时间线性扩张状态观测器(Finite-time linear extended state observer, FT-LESO), 它具有期望的收敛性能且结构简单、易于设计. 假设系统的状态无法量测, 观测器设计问题转化为扰动下的输出反馈控制问题. 针对该问题, 提出一种扰动下的有限时间线性输出反馈控制方法, 得到控制器参数与闭环系统状态向量2-范数间的解析关系. 在此基础上, 提出有限时间线性扩张状态观测器, 得到观测器参数与观测误差收敛速度及稳态观测误差间的解析关系, 给出一充分条件保证观测误差有限时间有界、且能以不低于指数收敛的速度收敛到给定范围内, 为观测器参数设计提供理论依据. 通过数值仿真验证提出的观测器, 仿真结果与理论分析相符, 提出的观测器是有效的.     

基于去随机化方法的Markov跳变系统有限频段控制

针对Markov跳变系统,本文利用去随机化方法将随机跳变系统转化为包含转移速率信息的确定系统,并讨论系统在给定时间内的控制问题,将特定频段干扰信号的频率信息引入控制器设计,以确保系统满足有限频段性能指标;同时从时间的角度设计给定时间控制器,使系统状态轨迹在工艺要求的时间内受限运动.所提方案不仅从频率、时间的尺度对系统频域特性及暂态性能进行综合分析,还充分考虑模态跳变对整体系统性能的影响,为降低现有设计方法的保守性提供了新的思路.最后仿真示例验证了所提方法的有效性及优越性.     

离散随机Markov跳跃系统有限时间有界控制

研究一类带乘性噪声的离散时间随机Markov跳跃系统的有限时间控制问题.首先,定义系统的有限时间稳定和有限时间有界,通过逐次迭代和条件期望给出系统有限时间稳定的充分必要条件;其次,针对含干扰的系统,利用Lyapunov方法和线性矩阵不等式技术得到系统有限时间有界的充分条件并设计状态反馈镇定控制器;然后,进一步考虑转移概率信息不完全下的有限时间有界问题;最后,通过数值例子验证了所提出方法的有效性.     

分数阶时变切换系统有限时间异步控制

针对一类时变切换系统,当考虑子系统具有分数阶(Fractional Order)特性时,提出了一种基于模型依赖平均驻留时间方法的有限时间稳定性条件及异步切换控制策略.借助Caputo分数阶导数引理和切换Lyapunov函数,利用矩阵不等式技术提出了分数阶时变切换系统有限时间稳定的充分条件.将有限时间稳定的结果进一步推广到有限时间有界的情形,利用平均驻留时间思想提出了分数阶时变切换系统有限时间有界的充分条件,基于该条件设计了系统的异步切换控制器.所给出的设计方法将系统异步切换控制问题转化为矩阵不等式组的求解问题.通过数值仿真验证了所提控制方法的有效性.     

基于有限时间观测器的混沌系统同步

根据有限时间稳定的定义,对混沌系统引入了有限时间观测器的概念,采用有限时间观测器实现混沌系统的同步,保证在给定的有限时间区间内,观测器状态与被观测系统的状态误差被限制在一个给定界内,从而达到观测系统状态的目的。利用线性矩阵不等式的方法,将观测器存在条件转化为求解系统的线性矩阵不等式。讨论了混沌系统同步的有限时间观测器的存在条件,并给出了观测器的具体设计。通过对Duffing-Holmes系统的同步仿真,验证了该方法的有效性。     

Optimal fault-tolerant control for Markov jump power systems with asynchronous actuator faults

Communication problems in the sensor-to-controller and controller-to-actuator channels can cause both the controller and actuator to run asynchronously with the original system in different operating modes. This paper investigates an optimal fault-tolerant control approach for Markov jump power systems (MJPSs) with asynchronous controller and actuator. Firstly, an asynchronous controller is proposed to deal with incomplete information (i.e., system modes) transmission in the sensor-to-controller channel. Secondly, a new asynchronous actuator faults model is constructed to simultaneously represent the two partial losses, of modes information in the controller-to-actuator channel, and of control effectiveness (LoCE) caused by actuator faults. Under this framework, two related hidden Markov models (HMMs) are formed, which reveal that both the controller and actuator are asynchronous with the controlled system in different modes. By using Lyapunov and optimal approaches, sufficient conditions are derived to ensure that MJPSs are mean square stable with an optimal guaranteed cost. Finally, Monte Carlo simulations are used to verify the effectiveness of the proposed control method.     

Markov跳变系统的非同步事件触发耗散容错控制

本文主要研究一类具有执行器故障的Markov跳变系统的非同步事件触发耗散容错控制问题.通过引入非同步事件触发器来降低传感器的采样数据传输频率,从而降低通信消耗.采用两个独立的隐Markov模型分别描述触发器、控制器与原系统之间的非同步现象.在此框架下,基于Lyapunov稳定性和耗散理论,得到了闭环控制系统在执行器存在故障的情况下随机稳定并严格耗散的充分条件.并借助矩阵不等式变换技术给出了触发器和控制器矩阵参数的求解方法,实现了触发器和控制器的协同设计.最后,通过仿真研究验证了所提出的设计方法的有效性.     

Quantized feedback stabilization of continuous-time Markov jump systems under asynchronous control

This paper addresses a new asynchronous control scheme for continuous-time Markov jump linear systems (MJLSs). Both controlled system and quantizer are asynchronous with the controller due to the process by which the controller can accurately observe and emit the switching signal being stochastic. The random variable satisfying Bernoulli distribution is introduced to describe this observation. On this basis, two methods are proposed to obtain sufficient conditions for exponential almost sure stability and almost surely asymptotically stability, respectively from the perspective of the linear matrix inequality (LMI). The results are independent of the asynchronous time interval. Finally, a numerical example demonstrates the validity and feasibility of developed theoretical results.     

Hybrid-triggered scheme asynchronous control for hidden Markov jump systems with partially unknown probabilities and cyber attacks

This paper is concerned with the issue of hybrid-triggered scheme $H_{\infty }$ asynchronous control for networked Markov jump systems (MJSs) with probabilistic cyber attacks. First, in view of the subsistent phenomenon that the controller cannot capture the system modes synchronously, the hidden Markov model (HMM) with partly unknown probabilities is introduced in this article to describe such asynchronous phenomenon. In addition, the hybrid-triggered scheme includes time-triggered scheme and event-triggered scheme, in which the switching signal between two schemes obeys random Bernoulli distribution. By utilizing Lyapunov stability theory and matrix inequality technique, some sufficient conditions are developed, which can guarantee the networked MJSs mean-square asymptotically stable (MSAS) and $H_{\infty }$ performance; also, the desired controller gains are obtained by singular value decomposition (SVD) methods. Moreover, as the special cases of the results above, three corollaries are given. Finally, a numerical example and a pulse width-modulation-driven boost converter (PWMDBC) model are provided to demonstrate the usefulness and reliability of our developed approaches.     

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。     

Static output feedback control for discrete‐time hidden Markov jump systems against deception attacks

This paper investigates the static output feedback control problem for Markov jump systems subject to asynchronous mode information and deception attacks. A hidden Markov model is employed to observe the unmeasurable system mode. In this case, the asynchronous phenomenon between the controller and the original system is depicted. By using the mode‐dependent Lyapunov function, a sufficient condition is established such that the resulting closed‐loop system is stochastically mean square exponentially ultimately bounded under randomly occurring deception attacks and external disturbance. Based on this condition, the asynchronous static output feedback controller is designed in view of linear matrix inequalities. Finally, the effectiveness and superiority of the presented method are elaborated via a numerical example and a practical example.     

Dissipativity‐based asynchronous control of discrete‐time Markov jump systems with mixed time delays

This paper addresses the problem of dissipativity‐based asynchronous control for a class of discrete‐time Markov jump systems. A unified framework to design a controller for discrete‐time Markov jump systems with mixed time delays is proposed, which is fairly general and can be reduced to a synchronous controller or a mode‐independent controller. Based on a stochastic Lyapunov function approach, which fully utilizes available information of the system mode and the controller, a sufficient condition is established to ensure the stochastic stability and strictly ( , , ) dissipative performance of the resulting closed‐loop system. Finally, the effectiveness and validity of the proposed method are illustrated with a simulation example.     

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.     

Extended state observer-based finite-region control for 2-D Markov jump systems

In this article, an extended state observer-based finite-region control scheme is presented for two-dimensional Markov jump systems with unknown mismatched disturbances. The mathematical model of the two-dimensional Markov jump systems is built on the well-known Roesser model. By establishing special recursive formulas and utilizing the 2-D Lyapunov function theory, sufficient conditions are obtained, which prove that the resultant system is finite-region bounded, if some linear matrix inequalities are achieved. Then, we provide an algorithm to solve the extended state observer-based controller gains. With the proposed control scheme, the external disturbances can be actively rejected from the system outputs. To conclude, a numerical example based on the Darboux equation is provided to demonstrate the validity and effectiveness of the devised control scheme.     

Robust extended dissipative control for sampled-data Markov jump systems

This paper investigates the problem of the sampled-data extended dissipative control for uncertain Markov jump systems. The systems considered are transformed into Markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach. The focus is on the design of a mode-independent sampled-data controller such that the resulting closed-loop system is mean-square exponentially stable with a given decay rate and extended dissipative. A novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality. The reduced conservatism of the criteria is demonstrated by two numerical examples. Furthermore, a sufficient condition for the existence of a desired mode-independent sampled-data controller is obtained by solving a convex optimisation problem. Finally, a resistance, inductance and capacitance (RLC) series circuit is employed to illustrate the effectiveness of the proposed approach.