Robust finite-time guaranteed cost control for impulsive switched systems with time-varying delay

This paper is concerned with the problem of robust finite-time guaranteed cost control for a class of impulsive switched systems with time-varying delay. Firstly, the definitions of finite-time boundedness, finite-time stabilization, and robust finite-time guaranteed cost control are presented. Next, based on the average dwell-time approach, sufficient conditions on robust finite-time guaranteed cost control are obtained for the uncertain impulsive switched systems. Then, by using multiple Lyapunov-like functional method and linear matrix equality (LMI) technique, the state feedback controller is designed to guarantee that the uncertain impulsive switched system is finite-time stabilized. Furthermore, a finite-time guaranteed cost bound is given. Finally, a numerical example is shown to illustrate the effectiveness of the proposed results.     

有限时间控制问题综述

有限时间控制系统因具有良好的鲁棒性能和抗扰动性能而受到广泛关注.首先,回顾了有限时间控制方法的起源,并列举了有限时间控制系统的几种常用判据;然后,总结了有限时间控制系统的研究现状;最后,讨论了未来可能的研究方向.     

On finite-time stability and stabilization of nonlinear port-controlled Hamiltonian systems

The finite-time stability and stabilization of nonlinear port-controlled Hamiltonian(PCH)systems are investigated in this paper,and a number of new results are proposed.Firstly,by exploiting the Hamiltonian structural properties,a proper form of the Hamiltonian function is obtained,based on which a finite-time stability criterion is then presented for a class of Hamiltonian systems.Secondly,using the obtained stability criterion and the so-called"energy shaping plus damping injection"technique,the continuous finite-time stabilization problem is studied for the PCH system,and several global stabilization results are provided.Finally,the continuous robust finite-time stabilization of the PCH system with external disturbances is investigated,and two results on designing global robust finite-time stabilizers are obtained.Study of several examples with numerical simulations shows that the control design approach developed in this paper works very well.     

New finite-time stability conditions of linear switched singular systems with finite-time unstable subsystems

ABSTRACT

This paper addresses the finite-time stability problem of linear switched singular systems with finite-time unstable subsystems. Dynamic decomposition techniques are used to transform such systems into equivalent one that is a reduced-order switched normal systems. Based on the mode-dependent average dwell time (MDADT) switching signal, new sufficient conditions are presented to guarantee the linear switched singular systems with finite-time unstable subsystems being finite-time stability, finite-time bounded and finite-time stabilization. Finally, a numerical example is employed to verify the efficiency of the preceding method.     

Finite-Time Observers: Application to Secure Communication

In this paper, control theory is used to formalize finite-time chaos synchronization as a nonlinear finite-time observer design issue. This paper introduces a finite-time observer for nonlinear systems that can be put into a linear canonical form up to an output injection. The finite-time convergence relies on the homogeneity properties of nonlinear systems. The observer is then applied to the problem of secure data transmission based on the finite-time chaos synchronization and the two-channel transmission method.      

具有有界时滞的脉冲随机泛函微分系统的有限时间稳定

本文研究了具有有界时滞的脉冲随机泛函微分系统的有限时间稳定和有限时间渐近稳定问题. 基于Lyap-unov函数、Razumikhin技巧以及平均脉冲区间条件, 本文建立了关于该系统有限时间稳定和有限时间渐近稳定的相关性准则. 最后, 给出例子说明结论的有效性.     

不确定广义大系统有限时间鲁棒分散控制

研究不确定连续广义大系统的有限时间鲁棒分散控制问题,设计系统的有限时间鲁棒分散状态反馈控制器.首先应用广义Lyapunov 函数法,给出不确定广义大系统有限时间鲁棒稳定的充分条件;其次,给出不确定广义大系统应用分散状态反馈控制器鲁棒镇定的充分条件和有限时间鲁棒分散控制器的设计方法;最后,通过仿真例子验证所提出方法的有效性.     

时变耦合复杂网络的有限时间广义外部同步

研究了两个具有时变耦合矩阵的复杂动态网络的有限时间广义外部同步的问题。设计了有限时间控制器, 使两个网络能在有限时间内实现外部同步。利用微分方程的有限时间稳定性理论,得到了复杂网络实现有限时间外部同步的充分条件。为了验证所提方案的有效性,给出了仿真算例,算例验证了有限时间广义外部同步方案的有效性。     

Finite-time output feedback control for a class of stochastic low-order nonlinear systems

This paper discusses the problem of finite-time stabilisation for a class of stochastic low-order nonlinear systems via output feedback. By generalising the adding a power integrator technique, constructing an implementable reduced-order observer and using the stochastic finite-time stability criterion, a finite-time output feedback controller is presented to guarantee that the closed-loop system is finite-time stable in probability. A simulation example is provided to verify the effectiveness of the proposed design method.     

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.     

On an output feedback finite-time stabilization problem

Studies the problem of finite-time output feedback stabilization for the double integrator system. A class of output feedback controllers that can achieve global finite-time stability for the double integrator system are constructed based on a “finite-time separation principle.” Furthermore, it is shown that the closed-loop system resulting from our control law can maintain its local finite-time stability regardless of some nonlinear perturbations. Thus, our control law actually applies to a large class of nonlinear second order systems     

离散线性切换系统的一致有限时间稳定分析和反馈控制及其在网络控制系统中的应用

研究了一类离散线性切换系统的一致有限时间稳定性分析和反馈镇定．基于线性矩阵不等式技术,给出了在任意切换信号作用下,离散线性切换系统有限时间稳定和有限时间有界的充分条件,并给出了离散线性切换控制系统一致有限时间状态反馈控制器的设计方法．将上述分析结果应用于一类丢包有界的网络控制系统,得到了保证其有限时间稳定的反馈控制器．最后,通过两个数值仿真例子验证了所提方法的有效性．     

Decentralised adaptive neural connectively finite-time control for a class of p-normal form large-scale nonlinear systems

ABSTRACT

This paper focuses on the decentralised adaptive finite-time connective stabilisation problem for a class of p-normal form large-scale nonlinear systems at the first. By combining the adding a power integrator technique, the neural network technique and the finite-time Lyapunov stability theory, the decentralised adaptive neural finite-time controllers are designed, which can guarantee the large-scale system is finite-time connectively stable. In order to avoid the effect of neural network estimation error on satisfying the finite-time criteria, the combination vectors are composed by the weights and the estimation errors of the neural networks. The maximal upper bounds of the combination vector norms are taken as the adaptive parameters. Because of employing neural networks, the restriction of the unknown nonlinear terms in some literature about finite-time control is relaxed. Two simulation examples are provided to prove the effectiveness and advantage of the proposed control method.     

机械系统的快速有限时间跟踪控制及其在航天器交会中的应用

针对一类具有匹配干扰的二阶机械系统,本文研究了快速有限时间跟踪控制问题.结合有限时间反步法和非奇异快速终端滑模,本文提出了一种新的快速有限时间控制律,并给出了控制器参数所需满足的充分条件以保证系统的快速有限时间稳定性.进一步地,在一定情形下,所设计的快速有限时间控制律能够退化为经典的反步法、有限时间控制律和非奇异快速终端滑模控制律.最终,将所设计的控制律应用于航天器交会系统,数值仿真结果验证了所提方法的有效性.     

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。     

Finite-time boundness of H ∞ filtering for switching discrete-time systems

For switched discrete-time systems, switching behavior always affect the finite-time stability property, which was neglected by most previous research. This paper investigated the problem of finite-time boundness of H _?? filtering for switched discrete-time systems. Sufficient conditions which can ensure finite-time bounded and H _?? filtering finite-time boundness under arbitrary switching are derived. Based on the results of finite-time boundness and stochastic character, the closed-loop system trajectory stays within a prescribed bound. An example is given to illustrate the efficiency of the proposed method.     

无刷直流电动机系统的有限时间同步

有限时间同步能够确保两个系统在有限的时间内实现同步,具有重要的研究意义.但常见的控制器往往只能确保两个系统渐近同步,而能够实现有限时间同步的控制器目前尚不多见,且存在控制器复杂,不连续易产生抖振现象等缺陷.为此,本文设计了一种简单连续的有限时间同步控制器,实现了主–从无刷直流电动机系统(the brushless DC motor system,BLDCM)的有限时间同步.首先建立了基于该控制器的主–从有限时间同步框架.然后,从理论上证明了两个相同的BLDCM系统有限时间同步的充分性同步判据.最后,通过数值实例验证了所得判据的有效性.     

An approach to design semi-global finite-time observers for a class of nonlinear systems

In this paper, the problem of designing semi-global finite-time observers for a class of nonlinear systems is investigated. Based on the theories of finite-time stability, an approach to designing semi-global finite-time observers for the nonlinear systems is presented. It has been shown that, after the finite time, the designed finite-time observer realizes the accurate reconstruction of the states of the nonlinear system. A numerical example is given to illustrate the effectiveness and validity of the met...     

考虑输入饱和的农用拖拉机路径跟踪有限时间控制

针对农用拖拉机的路径跟踪控制问题,提出基于有限时间和饱和技术的路径跟踪控制策略.首先,建立农机路径跟踪运动学模型,并通过有限时间控制技术,构造有限时间路径跟踪控制方法;其次,考虑到农用拖拉机的转向系统物理限制,将饱和技术与有限时间控制结合,给出复合的路径跟踪控制方法,通过严格的理论分析验证闭环系统在该控制器下的有限时间稳定性;最后,通过仿真结果表明,所设计的制导方法可以保证农用拖拉机快速、稳定地完成路径跟踪目标.     

Finite-time stability and instability of stochastic nonlinear systems

This paper presents a new definition of finite-time stability for stochastic nonlinear systems. This definition involves stability in probability and finite-time attractiveness in probability. An important Lyapunov theorem on finite-time stability for stochastic nonlinear systems is established. A theorem extending the stochastic Lyapunov theorem is also proved. Moreover, an example and a lemma are presented to illustrate the scope of extension. A useful inequality, extended from Bihari’s inequality, is derived, which plays an important role in showing the Lyapunov theorem. Finally, a Lyapunov theorem on finite-time instability is proved, which states that almost surely globally asymptotical stability is not equivalent to finite-time stability for some stochastic systems. Two simulation examples are given to illustrate the theoretical analysis.