Finite-time control of linear parameter-varying systems with norm-bounded exogenous disturbance

In this paper, a new approach is presented for finite-time control problems for linear systems subject to time-varying parametric uncertainties and exogenous disturbance. The disturbance is assumed to be time varying and bounded. Sufficient conditions are obtained for the existence of a linear parameter-dependent state feedback gain, which can ensure that the closed-loop system is finite-time bounded （FTB）. The conditions can be reduced to feasibility problems involving LMIs. Numerical examples show the validity of the proposed methodology.     

一类线性离散时间系统有限时间控制问题

讨论一类具有时变、有限能量外部扰动的线性离散时间系统的有限时间控制问题.首先研究问题可解的充分条件,并讨论了状态反馈控制器存在的条件,这些条件可归结为基于线性矩阵不等式(LMI)的可解性问题;然后给出状态反馈控制器和输出反馈控制器的具体设计;最后通过仿真验证了该方案的有效性.     

线性随机系统有限时间H∞ 控制

讨论一类具有时变、有限能量外部扰动的线性随机系统有限时间H∞控制问题．首先,给出了线性随机系统有限时间如控制问题的定义;然后,通过构造Lyapunov-Krasovskii函数,并结合线性矩阵不等式,给出了随机系统有限时间如控制器有解的充分条件;进一步,将该问题简化为具有线性矩阵不等式约束的优化问题,并给出了相应的求解算法;最后,通过数值算例表明了该设计方法的有效性．     

Finite-time disturbance attenuation of nonlinear systems

This paper is devoted to the finite-time disturbance attenuation problem of affine nonlinear systems. Based on the finite time Lyapunov stability theory, some finite-time H _∞ performance criterions are derived. Then the state-feedback control law is designed and the structure of such a controller is investigated. Furthermore, it is shown that the H _∞ controller can also make the closed-loop system satisfy finite-time H _∞ performance for nonlinear homogeneous systems. An example is provided to demonstrate the effectiveness of the presented results.     

Consensus of linear multi-agent systems with exogenous disturbance generated from heterogeneous exosystems

This paper addresses the consensus tracking problem for multi-agent linear systems subject to exogenous disturbances generated from heterogeneous exosystems. For the case that the disturbances are generated from linear heterogeneous exosystems, a linear disturbance observer and distributed control law are proposed, and sufficient condition for consensus tracking is established by combining the input-to-state stability and Lyapunov analysis methods. For the case when the disturbances are generated from non-linear heterogeneous exosystems, a non-linear disturbance observer is presented to estimate such disturbance by using the dynamic gain technique; then, a distributed control law is designed, and sufficient condition is also presented for achieving consensus tracking. Two simulation examples are provided to demonstrate the effectiveness of the proposed consensus protocols.     

Improved disturbance rejection for predictor-based control of MIMO linear systems with input delay

In this paper, we are concerned with the predictor-based control of multi-input multi-output (MIMO) linear systems with input delay and disturbances. By taking the future values of disturbances into consideration, a new improved predictive scheme is proposed. Compared with the existing predictive schemes, our proposed predictive scheme can achieve a finite-time exact state prediction for some smooth disturbances including the constant disturbances, and a better disturbance attenuation can also be achieved for a large class of other time-varying disturbances. The attenuation of mismatched disturbances for second-order linear systems with input delay is also investigated by using our proposed predictor-based controller.     

具有非匹配扰动的非线性变参数系统模型参考跟踪控制

本文研究了一类含有非匹配扰动的非线性变参数系统的跟踪控制问题.首先,设计非线性扰动观测器用于估计系统所受到的未知扰动.其次,在前馈–反馈跟踪控制器中引入扰动补偿控制项,提出一种基于扰动观测器的跟踪控制策略.利用依赖于状态和时变参数的线性矩阵不等式,导出保证闭环系统输入–状态稳定的充分条件,进而运用平方和凸优化技术解析地构造出扰动观测器和跟踪控制器.通过理论证明,所设计的控制策略能够实现非线性变参数系统输出对参考模型输出的跟踪,消除输出通道中非匹配扰动的影响.最后,由数值仿真例子验证了所提方法的有效性.     

Interval observer framework for fault-tolerant control of linear parameter-varying systems

This paper addresses the problem of passive fault-tolerant control for linear parameter-varying systems subject to actuator faults. The FTC, based on a linear state feedback, is designed to compensate the impact of actuator faults on system performance by stabilising the closed-loop system using interval observers. The design of interval observers is based on the discrete-time Luenberger observer structure, where uncertainties and faults with known bounds are considered. Sufficient conditions for the existence of the proposed observer are explicitly provided. Simulation results are presented to show the effectiveness of the proposed approach.     

连续时间线性脉冲系统的有限时间滤波

研究了连续时间线性脉冲系统的有限时间滤波问题。一方面给出了滤波误差系统有限时间稳定和满足性能要求的充分条件,并且给出了滤波器的设计方法。另一方面为了避免设计方法中出现的耦合问题,给出了另外两个结论。最后通过数值算例表明了结论的可行性和有效性。     

Finite-time stability of linear time-varying singular systems with impulsive effects

In this paper, we introduce a new concept of finite-time stability of linear time-varying singular systems with impulses at fixed times, and present new results for the above-mentioned class of system in the form of sufficient conditions. A sufficient condition is given in terms of matrix inequalities, which gives the opportunity of fitting the finite-time control problem in the general framework via impulsive control. A numerical example is presented to illustrate the efficiency of the proposed result.     

Anti‐disturbance control for nonlinear system via adaptive disturbance observer

This paper addresses the problems of disturbance estimation and anti‐disturbance control for nonlinear system with exogenous disturbance, which is generated from an unknown exogenous system. The state observer and the adaptive disturbance observer are designed, simultaneously. Compared with the existing methods, which assumed that the exogenous system parameter matrix was known, our disturbance observer is more applicable in practice. Utilizing the estimation information, an observer‐based dynamic output feedback controller is designed, which avoids the influence of output disturbance on the closed‐loop system, and contains a disturbance compensation term to compensate the input disturbance. Finally, simulations are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Flatness-based active disturbance rejection control for linear systems with unknown time-varying coefficients

A flatness-based active disturbance rejection control approach is proposed to deal with the linear systems with unknown time-varying coefficients and external disturbances. By selecting appropriate nominal values for the parameters of the system, all the deviation between the nominal and actual dynamics of the controlled process, as well as all the external disturbances can be viewed as a total disturbance. Based on the accurately estimated total disturbance with the aid of the proposed extended state observer, a linear proportional derivative feedback control law taking into account the derivatives of the desired output is designed to eliminate the effect of the total disturbance on the system performance. Finally, the load frequency control problem of a single-area power system with non-reheated unit is employed as an illustrative example to demonstrate the effectiveness of the proposed approach.     

一类非线性系统有限时间流形吸引的浸入与不变控制

本文对一类非线性系统,提出了一种设计渐近稳定控制律的有效方法.其中,通过更新系统浸入与不变流形理论的应用方法,流形的吸引坐标可以在有限时间内收敛到平衡点.为了得到闭环系统的稳定性,增广系统的各个信号被证明是有界的.本文得出的一个重要成果是流形吸引有限时间的计算方法.此外,在施加了有限时间流形吸引控制器之后,流形对外部有界未知扰动具有不敏感性.最后利用车摆系统来论述所提出的控制方法的设计步骤,以及通过仿真验证控制器的性能.     

关于一类脉冲切换系统的鲁棒H∞控制

研究一类具有扰动的脉冲切换线性系统的鲁棒H控制问题.分别从系统的鲁棒稳定性及其鲁棒性能两方面进行分析.首先利用Lyapunov函数法对系统的稳定性进行分析,给出了系统鲁棒渐近稳定的几个重要的充分条件,通过它很容易判断系统是否鲁棒稳定.进一步运用线性矩阵不等式(LMI)法对系统鲁棒性能进行分析,得到了一般系统的状态反馈矩阵和脉冲控制矩阵,并在此基础上得出了一个鲁棒H控制律.最后提出了一套基于MAT-LAB软件的鲁棒控制器的设计方法,并通过一个数值例子很好地验证了文中主要结论的有效性.     

Anti‐windup design of active disturbance rejection control for sampled systems with input delay

A novel anti‐windup design of active disturbance rejection control (ADRC) is proposed for industrial sampled systems with input delay and saturation. By using a generalized predictor to estimate the delay‐free system output, a modified extended state observer is designed to simultaneously estimate the system state and disturbance, which could become an anti‐windup compensator when the input saturation occurs. Accordingly, a feedback controller is analytically designed for disturbance rejection. By proposing the desired closed‐loop transfer function for the set‐point tracking, a prefilter is designed to tune the tracking performance while guaranteeing no steady‐state output tracking error. A sufficient condition for the closed‐loop system stability is established with proof for practical application subject to the input delay variation. Illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control design.     

状态滞后线性系统的H∞状态反馈控制器

利用LMI(线性矩阵不等式 )的方法, 首先给出了一般的状态滞后自治系统内稳定且具有H_∞范数界的一个充分条件. 并由此得到了一般的状态滞后系统H_∞问题有解的一个充分条件, 通过解LMI可以获得控制器的解. 最后举例说明方法的正确性.     

Event‐triggered control for discrete‐time linear systems subject to bounded disturbance

This paper considers event‐triggering controller design for directly observable discrete‐time linear systems subject to bounded disturbances. The main control objective is diminishing the influence aroused by the disturbances despite a reduction of the communication. Criteria are given to design feedback controllers in order to guarantee that systems are uniformly ultimately bounded in an ellipsoidal‐positive invariant set, which is used as an estimate of control performance for disturbance rejection. An optimization for minimizing the ellipsoidal‐positive invariant set is achieved by synthesizing the feedback control gain and the given event‐triggering conditions in LMIs. The effectiveness and applicability of the controller are illustrated by simulations and experimental implementations. Copyright © 2015 John Wiley & Sons, Ltd.     

Simultaneous fault-tolerant control and disturbance rejection for systems with fault in polynomial form

This article studies the simultaneous fault-tolerant control and disturbance rejection for systems with fault in polynomial form. The unknown external disturbance is considered to be caused by the external source system, and the fault can be expressed as a polynomial function of time. Combining the fault observer and the disturbance observer, a controller is designed, which can not only diagnose the fault, but also improve the anti-disturbance performance. Finally, a numerical example is given to verify the validity of the results.     

Discrete-time H∞ control of linear parameter-varying systems

We introduce new conditions for the H_∞ synthesis of discrete-time linear parameter-varying systems in the form of linear matrix inequalities. A distinctive feature of the proposed conditions is the ability to handle variation in both the dynamics and the input matrices without resorting to dynamic augmentation or iterative procedures. We show that this new condition contains the existing poly-quadratic H_∞ synthesis result as a particular case. We also derive a corollary which shows improvement even in the stronger case of quadratic H_∞ synthesis. Additionally, we show that, surprisingly, a dynamic gain-scheduled quadratic H_∞ controller can result in inferior performance compared to a static robust controller. Numerical examples illustrate our results.