MIMO非线性最小相位系统的光滑调节

本文研究多输入多输出非线性最小相位系统的光滑调节问题,得到的主要结论是:对合的在原点具有相对阶的局部双曲最小相位系统能渐近跟踪满足某种有界条件的局部Lyapunov稳定的信号.一类具有一致相对阶的全局指数稳定的最小相位系统,若满足某种类似的Lipschitz条件,则能渐近跟踪一类很广泛的信号,既可以是Poisson稳定的,也可以是无界的.     

经输出动态反馈的非线性奇异系统输出调节问题

讨论非线性奇异系统的输出调节问题,在没有可正常化的假设条件下,给出了降阶的正常状态空间的输出动态反馈控制器的设计,并导出了这种控制器存在的充分必要条件.     

基于神经网络的非线性系统的输出调节

非线性系统输出调节问题可解的充要条件是存在一个中心流形满足某个非线性偏微分方程。本文用多层前向神经网络求解该非线性偏微分方程，从而逼近非线性系统的中心流形。在此基础上，构造状态反馈控制律，实现非线性系统的输出调节。     

具有自适应内模的一类非线性系统输出调节问题

研究一类包含未知非线性项的非线性系统的鲁棒输出调节问题.此类非线性系统由一包含未知参数的线性中性稳定的外系统驱动.首先运用调节器方程组解和标准内模将输出调节问题转化为镇定问题;然后给出控制律镇定闭环系统,同时利用镇定输入项和外系统信息设计出自适应内模方程.控制律使得闭环系统的信号全局最终有界,且误差被调节至预先设定的任意小的精度值.仿真结果验证了所提出设计方法的有效性.     

非线性系统的输出调节与受控中心流形

本文用中心流形理论＾［７］及动力系统方法＾［８］，考虑了一般非线性系统的输出调节问题，在弱于Ｉｓｉｄｏｒｉ和Ｂｙｒｎｅｓ＾［６］的条件下，得到了这问题可解的充分必要条件。     

变结构控制实现非线性系统的输出调节和鲁棒输出调节

对于确定性的和受到结构扰动的非线性系统，用变结构控制设计的控制律能够满足到达条件，构造的切换面能产生稳定的滑动模态。当非线性系统在切换面上运动时，可以实现输出调节和鲁棒输出调节。     

具有一般不确定性的非线性系统的鲁棒输出反馈控制

为将文献「１」中结果推广到具有一般不确定性的系统并降低在过渡阶段所需要的控制量,通过引入新的正则信号和一些正光滑设计函数来处理状态估计误差和不确定性,设计了鲁棒输出反馈控制器,它能保证闭环系统信号的全局有界性,并使输出跟踪误差任意小,仿真说明,应用本文控制器,获得的性能更好,所需控制量要小。     

非线性控制系统的全局输出调节

讨论了非线性控制系统的全局输出调节.首先推广精确线性化方法,通过状态反馈 和微分同胚将非线性系统的全局输出调节问题,转化为线性系统对非线性系统的跟踪问题. 通过提出可解性的概念,得到线性系统对非线性系统全局跟踪的条件,该结果是线性系统结 果的推广.在反馈同胚变换全局成立条件下,得到非线性控制系统全局输出调节问题的充分 条件,该条件对外部系统只做较弱的可解性假设,在反馈同胚变换局部成立的条件下,可得局 部结果.     

离散时间非线性最小相位系统的动态输出反馈镇定

研究了离散时间非线性最小相位系统的动态输出反馈镇定.首先对离散时间非线性系统引入了逼近渐近稳定性的概念.基于此概念,提出了一种动态补偿器设计的新方法.主要结果是,如果一非线性系统的零动态是逼近渐近稳定的,则能用动态输出反馈镇定.动态补偿器的设计是构造性的.     

基于奇异摄动理论的非仿射系统的输出调节问题

基于奇异摄动的时标分解理论和动态逆设计的方法,研究了一类非仿射非线性系统的输出调节问题.通过将控制律定义为一个快动态系统的解,得到了指数稳定的误差系统状态方程,从而实现了原系统的输出相对于外系统的参考信号具有零误差的跟踪效果.结果表明在满足标准假设和一组偏微分方程有解的前提下,该输出调节问题是可解的.仿真实例表明了该理论方法的有效性.     

Global output regulation for output feedback systems with an uncertain exosystem and its application

This paper presents the solvability conditions for the global robust output regulation problem for a class of output feedback systems with an uncertain exosystem by using output feedback control. An adaptive control technique is used to handle the unknown parameter vector in the exosystem. It is shown that this unknown parameter vector can be exactly estimated asymptotically if a controller containing a minimal internal model is employed. The effectiveness of our approach has been illustrated by an asymptotic tracking problem of a generalized fourth‐order Lorenz system. Copyright © 2009 John Wiley & Sons, Ltd.     

非最小相位系统跟踪控制综述

非最小相位系统是指包含不稳定零动态的系统.经典的跟踪控制理论,特别是非线性系统跟踪控制理论,是以最小相位系统为基础建立的,不能直接用于非最小相位系统.研究非最小相位系统跟踪控制理论,是对经典控制理论的扩展和补充,具有重要的意义.本文对目前非最小相位系统跟踪控制领域取得的成果进行综述.首先梳理各种非最小相位系统跟踪控制方法的基本思想,并按照近似跟踪和精确跟踪进行归类,建立非最小相位系统跟踪控制的基本框架.然后围绕该框架对各种方法进行详细介绍.接着讨论非最小相位系统的跟踪性能限制.最后总结现有研究存在的一些问题及对今后的发展方向进行展望.本文的目的在于使控制工作者对非最小相位系统的跟踪控制有一个较为清晰的认识.     

Robust output regulation of minimum phase nonlinear systems using conditional servocompensators

We consider the design of a robust continuous sliding mode controller for the output regulation of a class of minimum‐phase nonlinear systems. Previous work has shown how to do this by incorporating a linear servocompensator in the sliding mode design, but the transient performance is degraded when compared to ideal sliding mode control. Extending previous ideas from the design of ‘conditional integrators’ for the case of asymptotically constant references and disturbances, we design the servocompensator as a conditional one that provides servocompensation only inside the boundary layer; achieving asymptotic output regulation, but with improved transient performance. We give both regional as well as semi‐global results for error convergence, and show that the controller can be tuned to recover the performance of an ideal sliding mode control. Copyright © 2005 John Wiley & Sons, Ltd.     

Nonlinear output regulation for invertible nonlinear MIMO systems

In this paper, we address the problem of output regulation for a broad class of multi‐input multi‐output (MIMO) nonlinear systems. Specifically, we consider input–affine systems, which are invertible and input–output linearizable. This class includes, as a trivial special case, the class of MIMO systems which possess a well‐defined vector relative degree. It is shown that if a system in this class is strongly minimum phase, in a sense specified in the paper, the problem of output regulation can be solved via partial‐state feedback or via (dynamic) output feedback. The result substantially broadens the class of nonlinear MIMO systems for which the problem in question is known to be possible. Copyright © 2015 John Wiley & Sons, Ltd.     

Global asymptotic tracking for nonminimum‐phase nonlinear systems in output feedback form

The problem of global asymptotic tracking by output feedback is studied for a class of nonminimum‐phase nonlinear systems in output feedback form. It is proved that the problem is solvable by an n‐dimensional output feedback controller under the two conditions: (a) the nonminimum‐phase nonlinear system can be rendered minimum‐phase by a virtual output; and (b) the internal dynamics of the nonlinear system driven by a desired signal and its derivatives has a bounded solution trajectory. With the help of a new coordinate transformation, a constructive method is presented for the design of a dynamic output tracking controller. An example is given to validate the proposed output feedback tracking control scheme.     

Output regulation for a class of uncertain nonlinear systems with nonlinear exosystems and its application

In this paper, we consider the global robust output regulation problem for a class of uncertain nonlinear systems with nonlinear exosystems. By employing the internal model approach, we show that this problem boils down to a global robust stabilization problem of a time-varying nonlinear system in lower triangular form, the solution of which will lead to the solution of the global robust output regulation problem. An example shows the effectiveness of the proposed approach.     

不确定非线性系统的鲁棒自适应输出反馈控制

基于自适应非线性阻尼,提出一种鲁棒自适应输出反馈控制方法。该方法适用于带有未建模动态、未知非线性、有界扰动、未知非线性参数和不确定控制系数的多输入多输出非线性系统。理论证明,在一定的假设条件下,该方法能保证闭环系统所有动态信号有界;不论有多少不确定非线性参数、多高阶的非线性系统,只需要一个自适应控制参数和观察参数;而且通过选择适当的控制器和观测器参数,能使控制误差和估计误差达到任意小。仿真结果表明了所提出方法的有效性。     

Certainty equivalence in nonlinear output regulation with unmeasured error

In this article, we consider a nonlinear output regulation problem in which the controlled output and the measured output are not the same. It is assumed that the controlled plant has a single control input, and that it can be transformed into Gauthier–Kupka's observability canonical form. Then, it is shown that a design based on certainty equivalence is effective for determining a controller that solves the given problem.     

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.     

一类非线性输出反馈系统的自适应输出调节问题

本文讨论一类非线性系统的全局鲁棒输出调节问题.假定被控非线性系统的系统输入方向未知,且产生参考或扰动信号的外部系统含未知参数,这为控制律的设计带来了挑战.文章使用自适应控制方法和内模原理,解决了一类相对阶为1的非线性输出反馈系统的输出调节问题,并将结果应用于处理Lorenz系统的渐近跟踪问题.