Cooperative output synchronisation of networked feedforward nonlinear systems via linear sampled-data control

This paper studies the problem of cooperative output synchronisation of networked feedforward nonlinear systems via linear sampled-data control. To dominate the unknown nonlinear perturbing terms, a scaling gain is introduced by a change in coordinates. Then, we construct a reduced-order sampled-data observer and use the backstepping method to design a linear sampled-data controller. By using combined graph theory with feedback domination approach, an explicit formula for the sampling period can be obtained under the proposed controller with appropriate gains such that all outputs of the agents in the network can be synchronised. Finally, two examples are provided to verify the effectiveness of the proposed method.     

非线性微分-代数系统的输出反馈镇定:基于线性采样控制

对满足指数1和线性增长条件的非线性微分-代数系统,本文证明其采样输出反馈镇 定控制问题可解.首先,给出一个线性显式非初始化状态观测器设计;然后,构造出线性的采样输出 反馈控制器,使得整个闭环系统渐近稳定.仿真结果表明了所提控制方法的有效性.     

Global practical tracking of a class of nonlinear systems using linear sampled-data control

This paper considers the problem of global practical tracking via sampled-data control for a class of uncertain nonlinear systems. Under a lower triangular linear growth condition, a sampled-data state feedback controller is first constructed such that the states are globally bounded and the error between the system output and the reference signal will be rendered smaller than a given tolerance. When only the output of the system is measurable, a sampled-data output feedback controller, whose observer and control law are both linear, is constructed to solve the global practical tracking problem.     

Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems

This paper studies sampled-data output feedback control of a class of nonlinear systems. It is shown that the performance of a stabilizing continuous-time state feedback controller can be recovered by a sampled-data output feedback controller when the sampling period is sufficiently small. The output feedback controller uses a deadbeat discrete-time observer to estimate the unmeasured states. Two schemes are proposed to overcome large initial transients when the controller is switched on.     

Application of the dynamic high‐gain scaling methodology to servocompensator design

The error‐feedback servomechanism problem is addressed for a general class of strict‐feedback‐like systems. We provide two error‐feedback control designs based on our recent results on adaptive output‐feedback based on dynamic high‐gain scaling. One control design is of a dual high‐gain observer/controller structure, whereas the other control design utilizes a backstepping‐based controller in conjunction with a dynamic high‐gain scaling‐based observer. Owing to the particular robustness properties offered by a dynamic high‐gain scaling‐based controller and a backstepping‐based controller, the two designs require slightly different sets of assumptions on the system. Both design techniques allow the system to contain both unknown functions and uncertain appended input‐to‐state stable dynamics. Copyright © 2008 John Wiley & Sons, Ltd.     

Global finite-time stabilization for a class of switched nonlinear systems via output feedback

This paper addresses the problem of global finite-time stabilization for a class of uncertain switched nonlinear systems via output feedback under arbitrary switchings. Based on the adding a power integrator approach, we design a homogeneous observer and controller for the nominal switched system without the perturbing nonlinearities. Then, a scaling gain is introduced into the proposed output feedback stabilizer to implement global finite-time stability of the closed-loop system. In addition, the proposed approach can be also extended to a class of switched nonlinear systems with upper-triangular growth condition. Two examples are given to illustrate the effectiveness of the proposed method.     

Adaptive Output Feedback Control for a Class of Uncertain Stochastic Nonlinear Systems With Unknown Time‐Delays

This paper investigates the problem of output feedback control for a class of stochastic nonlinear systems with time‐delays. Using dynamic gain scaling technique, an adaptive update law is introduced to the observer and controller to deal with the unknown parameters. Based on the Lyapunov‐Krasovskii functional and stochastic Barbalat's lemma, it is proved that the proposed universal‐type adaptive output feedback controller can regulate all the states of the closed‐loop system almost surely. A simulation example is presented to illustrate the effectiveness of the proposed design procedure.     

Global control of nonlinear systems with uncertain output function using homogeneous domination approach

This paper addresses the problem of using output feedback to globally control a class of nonlinear systems whose output functions are not precisely known. First, for the nominal linear system, we design a homogeneous state compensator without requiring precise information of the output function, and construct a nonlinear stabilizer with adjustable coefficients by using the generalized adding a power integrator technique. Then based on the homogeneous domination approach, a scaling gain is introduced into the proposed output feedback controller, which can be used by tuning the scaling gain to solve: (i) the problem of global output feedback stabilization for a class of upper‐triangular systems; and (ii) the problem of global practical output tracking for a class of lower‐triangular systems. Copyright © 2011 John Wiley & Sons, Ltd.     

基于观测器的一类连续非线性系统的采样控制

首先使用反演方法分别设计了系统的连续时间状态反馈控制器、连续时间观测器和基于连续时间观测器的连续时间控制器. 接下来, 利用零阶保持法对连续时间状态反馈控制器进行离散化, 获得了状态反馈采样控制器; 利用零阶保持法对基于连续时间观测器 的连续时间控制器离散化, 获得了基于连续时间观测器的采样控制器; 利用Euler法对连续时间观测器离散化, 同时利用零阶保持法对控制器离散化, 从而获得了采样观测器和基于采样观测器的采样控制器. 本文论证了上述状态反馈采样控制器和基于连续时间观测器的采样控制器可以保证闭环系统渐近稳定, 而基于采样观测器的采样控制器可以保证被控对象的状态是有界的, 其最终边界依赖于设计参数与采样周期. 最后, 通过选择适当的采样周期, 完成了闭环采样控制系统的设计. 一个船舶航向控制的例子表明应用本文 所提方法设计出的三种采样控制器具有良好的控制效果.     

Stabilization of a nonlinear jump system

In this paper we consider the problem of output feedback stabilization of a general nonlinear jump system. We shall show that the combination of a locally asymptotically stabilizing state feedback law and a local asymptotic observer yields a locally asymptotically stabilizing output feedback controller. Hence, the local separation principle holds for the nonlinear jump system. This result can be applied to nonlinear sampled-data systems.     

一类非线性状态时滞系统的基于采样控制器的渐近稳定问题

针对一类含有状态时滞的非线性系统,利用采样控制方法研究其渐近稳定问题.解决这一问题的关键在于对系统时滞的处理,以及对由于采样方法而产生的状态增长误差进行估计.由于所考虑的时滞是常时滞,可以利用分割方法对系统时滞进行分割,将时滞划分成与采样时间长度相同的数个时间区间,并基于这种分割,通过数学归纳法对系统状态增长误差进行估计.通过坐标变换引入一个比例增益压制系统的非线性项,然后设计含有比例增益的状态采样观测器和采样控制器,结合非线性时滞系统的Lyapunov泛函方法分析闭环系统的稳定性,最终确定比例增益和采样时间需要满足的条件,以保证闭环系统的渐近稳定性.最后通过数值例子表明所用研究方法以及所得研究结果是有效的.     

Global sampled-data output feedback stabilisation for a class of nonlinear systems with unknown output function

This paper discusses the problem of global sampled-data output feedback stabilisation for a class of nonlinear systems whose output function is unknown. A systematic design scheme is developed to construct a linear output feedback control law in sampled-data form. An explicit formula for the maximum allowable sampling period is computed to guarantee global stability of the uncertain nonlinear systems under the proposed controller with appropriate gains. Two examples are given to demonstrate the effectiveness of the proposed design procedure.     

Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems

This article considers the problem of global finite-time stabilisation by output feedback for a class of nonlinear systems comprised of a chain of power integrators perturbed by an uncertain vector field. To solve the problem, we first construct a homogeneous observer and controller in a recursive way for the nominal system without the perturbing nonlinearities. Then, using the homogeneous domination approach, we scale the homogeneous observer and controller with an appropriate choice of gain to render the uncertain nonlinear system globally finite-time stable. Due to the use of a reduced-order observer, the proposed output feedback controller is applicable to those systems with unknown gains associated with the power integrators.     

Adaptive output feedback regulation for a class of uncertain nonlinear systems

In this paper, the problem of global state regulation by output feedback is investigated for a class of uncertain nonlinear systems satisfying some relaxed upper‐triangular‐type condition. Using a linear dynamic gain observer with two dynamic gains and introducing two appropriate change of coordinates, we give a constructive design procedure for the linear‐like output feedback stabilizing controller. It is proved that the proposed controller globally regulates all the states of the uncertain system and maintains global boundedness of the closed‐loop system. An example is provided to demonstrate the effectiveness of the proposed design scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Global output feedback stabilisation of nonlinear systems with a unifying linear controller structure

We investigate the problem of global stabilisation by linear output feedback for a class of uncertain nonlinear systems with zero-dynamics. Compared with the previous works, new dilation-based assumptions are introduced that allow the system nonlinearities and its bounding functions to be coupled with all the states. The nonlinear systems of this paper can be considered as an extended form of some low triangular and feedforward systems. Dynamic gain scaling technique is applied to the controller design and stability analysis. It is proved that with a unifying linear controller structure and flexible adaptive laws for the observer gain, global stabilisation of the nonlinear systems can be achieved.     

Observer-based H-infinity output feedback control with feedback gain and observer gain variations for Delta operator system

Considering that the controller feedback gain and the observer gain are of additive norm-bounded variations, a design method of observer-based H-infinity output feedback controller for uncertain Delta operator systems is proposed in this paper. A sufficient condition of such controllers is presented in linear matrix inequality （LMI） forms. A numerical example is then given to illustrate the effectiveness of this method, that is, the obtained controller guarantees the closed-loop system asymptotically stable and the expected H-infinity performance even if the controller feedback gain and the observer gain are varied.     

Robust observer design for nonlinear uncertain systems with LQ regulators

For a class of uncertain systems with linear nominal dynamics and nonlinear uncertainties, it has been shown (Katayama and Sasaki 1987) that linear quadratic (LQ) state feedback regulators can be used to provide robust asymptotic stability. In this paper, we study the combined observer-controller design problem, based on the linear state feedback regulator proposed by Katayama and Sasaki (1987), so that only output feedback is needed. Both full-order and reduced-order observers are considered. For the full-order observer, we propose an algorithm to synthesize the robust observer gain matrix. It is shown that with the observer it is still possible to achieve robust asymptotic stability. For the reduced-order observer, some conditions are derived to guarantee the robust asymptotic stabilizability of the uncertain systems. The trade-off between the magnitudes of controller and observer gains is clear in our approach. An example is used to illustrate the design process of the robust controller with full-order as well as reduced-order observers.     

一类非线性系统的控制器和观测器设计

研究一类非线性系统的全状态反馈控制问题、观测器设计问题及输出反馈控制设计问题.首先设计出非线性全状态反馈控制器,获得了系统指数镇定的充分条件.然后提出了非线性观测器,并证明了该观测器是指数稳定观测器.进一步,在控制器和观测器问题的充分条件满足的假设下,证明了提出的带估计状态的反馈控制能达到指数镇定.最后,仿真实例验证了所得结果的有效性.     

Output feedback control of a class of feedforward nonlinear systems in the presence of sensor noise

We propose an output feedback controller for a class of feedforward nonlinear systems under sensor noise. The sensor noise is any signal whose DC component is finite, which covers not only deterministic signals but also random signals including many practical noises. We introduce a notion of virtual state, then propose a measurement output feedback controller that utilizes a gain scaling factor. The gain scaling factor is commonly employed by the observer and controller. Through analysis, we show that all system states and output remain to be bounded in the presence of sensor noise, and the bound of states except output can be made arbitrarily small. Moreover, if the DC component of sensor noise is zero, the ultimate bound of the states and output can be made arbitrarily small by increasing the gain scaling factor in the presence of sensor noise. Copyright © 2013 John Wiley & Sons, Ltd.