Fixed-time output regulation of linear delay systems by smooth time-varying control

This article investigates the fixed-time output regulation problem (FxTORP) for linear systems in the presence of input delay. A linear controller consisting of the linear periodic delayed feedback (PDF) gain and the feedforward gain obtained by solving regulator equations is designed, such that FxTORP is addressed. If only the measurable output can be used for feedback, a linear observer with periodic coefficient and artificial delay is designed so that its state converges to the state of the augmented system at a prescribed finite time. Based on the estimated state, the output regulation problem can also be solved by using observer-based output feedback. The most significant advantages of this article are that the PDF gain can be taken as smooth and the output regulation problem is achieved within a prespecified regulation time. Finally, a simulation example is given to substantiate the validity of the proposed approaches.     

线性系统的事件触发输出反馈有限时间有界控制

本文研究了线性系统的事件触发输出反馈有限时间有界控制问题. 与渐近稳定只定性地要求系统在采样间隔 有界不同, 有限时间有界需要估计系统轨迹的上界以保证满足动态系统的定量要求. 本文基于类李雅普诺夫函数给出了 保证闭环系统的有限时间有界性和避免芝诺现象的充分条件. 这些充分条件可以转化为线性矩阵不等式, 便于验证和实 际应用. 此外, 为了节约资源, 提出了一种可变参数的事件触发规则, 提高了设计灵活性. 仿真结果验证了本文的主要结 论.     

Practical output regulation for bounded linear infinite-dimensional state space systems

We develop the mathematical foundations of practical state space output regulation for bounded infinite-dimensional linear systems. By practical output regulation we mean asymptotic tracking of references and rejection of disturbances with a given accuracy. Our main results are general upper bounds for the norms perturbations to the parameters of the exosystem, the plant and a controller which achieves exact output regulation. These bounds depend explicitly on the desired tracking accuracy ε>0. In this paper, all perturbations are assumed to be bounded, additive and linear. Our results apply for both feedforward and error feedback controllers, and for arbitrary bounded uniformly continuous reference/disturbance signals.     

带有干扰的挠性卫星非线性姿态输出反馈控制

针对挠性卫星在飞行过程中存在参数不确定性、干扰（常值扰动和正弦扰动）及挠性附件的振动控制问题,提出了一类基于输出反馈控制系统的鲁棒设计方法,该设计仅利用姿态四元数输出信息,而无需角速度、挠性变形位移及其速率测量信息;同时,在控制中又引入积分环节用于减小常值干扰引起的稳态误差,并且控制器参数的选者并不依赖于系统参数,基于Lyapunov理论证明了所设计的控制器保证了姿态的稳定和模态振动的衰减;最后,将该方法应用于挠性卫星的姿态机动控制,仿真结果表明该控制器不仅对参数不确定性具有很好的鲁棒性,而且能够有效消除常值干扰和正弦干扰的影响,在完成姿态机动控制的同时,能够抑制挠性附件的结构振动,具有良好的过渡过程品质．     

Trajectory‐keeping in satellite formation flying via robust periodic learning control

This paper proposes an iterative learning control (ILC) scheme to ensure trajectory‐keeping in satellite formation flying. Since satellites rotate the earth periodically, position‐dependent disturbances can be considered time‐periodic disturbances. This observation motivates the idea of repetitively compensating for external disturbances such as solar radiation, magnetic field, air drag, and gravity forces in an iterative, orbit‐to‐orbit manner. It is shown that robust ILC can be effectively utilized for satellite trajectory tracking, thus enabling time‐variant formation flying between the leader‐ and follower‐satellites. The validity of the results is illustrated through computational simulations. Copyright © 2009 John Wiley & Sons, Ltd.     

Finite-time stability and stabilisation of singular discrete-time linear positive systems with time-varying delay

ABSTRACT

In this paper, the problem of finite-time stability and stabilisation for positive singular discrete-time linear systems with time-varying delay is investigated. We first present novel delay-dependent sufficient conditions for positivity and finite-time stability of the unforced systems. We then apply the obtained results to solve finite-time stabilisation problem of the considered systems. The sufficient conditions for the positivity and finite-time stabilisable of such systems are formulated in terms of a standard linear programming (LP) problem. Numerical examples are provided to illustrate the effectiveness and advantages of our results.     

Solutions to the output regulation problem of linear singular systems

In this paper, we revisit the output regulation problem for linear singular systems and identify an important case of the general regulation problem where the measurement output is identical to the vector to be regulated. We derive a necessary and sufficient condition for the regulation problem to be solvable via either full information feedback or error feedback. Then we show how full information feedback and error feedback controllers can be constructed explicitly.     

Cooperative linear output regulation for networked systems by dynamic measurement output feedback

This paper investigates the cooperative linear output regulation problem of a class of heterogeneous networked systems with a common reference input but with different disturbances for individual nodes. A novel distributed control law is presented based on dynamic measurement output feedback. It is shown that the overall networked closed-loop control system is asymptotically stable and the output regulation errors asymptotically approach zero as time goes to infinity under a sufficient and necessary condition. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed control law.     

Almost output regulation of switched linear dynamics with switched exosignals

For systems with switched linear dynamics and affected by persistent switched exosignals, we propose a new hybrid control approach to achieve not only closed‐loop stability but also tracking and/or rejection of persistent references/disturbances generated by multiple exosystems, namely, output regulation. It is assumed that both controlled plant and exosystem are described by switched linear models. The proposed hybrid controller/output regulator is specified as a switching impulsive system, where the controller states will undergo impulsive jumps at each switching instant. Based on the average dwell time switching technique, it has been shown how to completely reduce the synthesis problem of the hybrid controller to a set of linear matrix equations and linear matrix inequalities. Both continuous‐time and discrete‐time cases are discussed. To demonstrate its usefulness, the proposed hybrid control method has been applied to solve the output regulation problem for a mechanical system. Copyright © 2017 John Wiley & Sons, Ltd.     

Semi-global output regulation for linear systems with input saturation by composite nonlinear feedback control

To improve transient performance of output response, this paper applies composite nonlinear feedback (CNF) control technique to investigate semi-global output regulation problems for linear systems with input saturation. Based on a linear state feedback control law for a semi-global output regulation problem, a state feedback CNF control law is constructed by adding a nonlinear feedback part. The extra nonlinear feedback part can be applied to improve the transient performance of the closed-loop system. Moreover, an observer is designed to construct an output feedback CNF control law that also solves the semi-global output regulation problem. The sufficient solvability condition of the semi-global output regulation problem by CNF control is the same as that by linear control, but the CNF control technique can improve the transient performance. The effectiveness of the proposed method is illustrated by a disturbance rejection problem of a translational oscillator with rotational actuator system.