匹配条件不满足时线性系统未知输入观测器设计

针对一类不满足观测器匹配条件的线性系统,讨论了未知输入观测器设计方法.首先,为了突破观测器匹配条件的限制,提出了一种与未知输入相对阶无关的辅助输出构造方法.然后,把未知输入看作系统状态的一部分,将原系统转化为一个不含未知输入的增维线性描述系统.针对这样的系统转化,对一系列等价前提条件进行了详细的讨论.之后,针对该增维线性描述系统,构造Luenberger观测器来估计原系统的状态和未知输入.同时,借助于高阶滑模微分器,来估计辅助输出中的未知信号.最后,对一个单连杆柔性机械手模型进行了数值仿真,仿真结果表明了方法的有效性.     

Trigger‐based tracking control for a class of uncertain nonlinear systems via an event‐triggered extended state observer

An event‐triggered observer‐based output feedback control issue together with triggered input is investigated for a class of uncertain nonlinear systems subject to unknown external disturbances. Two separate event‐triggered conditions are located on the measurement channel and control channel, respectively. An event‐triggered extended state observer (ETESO) is employed to estimate unmeasurable states and compensate uncertainties and disturbances in real time while it is not required for real‐time output measurement. Then, combined with backstepping method and active disturbance rejection control, an output feedback control scheme is proposed, where an event‐triggered input is developed for reducing the communication rate between the controller and the actuator. The triggered instants are determined by a time‐varying event‐triggered condition. Two simulations, including a numerical example and an permanent‐magnet motor, are illustrated to verify the effectiveness of the proposed schemes.     

Algebraic conditions for state equivalence to a discrete-time nonlinear observer canonical form

Algebraic necessary and sufficient conditions for a single output discrete-time system to be state equivalent to a (generalized) nonlinear observer canonical form with (or without) output transformation are derived. Our algebraic conditions are easier to verify for researchers unaccustomed to differential geometry. In addition, our proofs are constructive and contain the state and output transformations for (generalized) nonlinear observer canonical forms.     

无未知参数先验信息的非线性自适应观测器设计

研究了一类具有未知参数的非线性系统自适应观测器设计问题．不同于现有结果,本文所研究的非线性系统更为。一般,已知的系统信息更少：1）系统未知参数的范数的上界未知;2）具有关于可测输出非Lipschitz连续的非线性动态;3）系统输出显式地依赖于控制输入．通过设计自适应调节器来估计未知参数范数,从而给出了不基于未知参数先验信息的非线性自适应观测器设计的新方法．所设计的观测器为令局渐近收敛的,即实现了系统状态的渐近重构,确保了未知参数估计的一致有界性．此外,在系统输出不显式地依赖于控制输入的条件下,研究了降维观测器的设计问题．仿真例子验证了本文理论结果的正确性．     

无未知参数先验信息的非线性自适应观测器设计

研究了一类具有未知参数的非线性系统自适应观测器设计问题.不同于现有结果,本文所研究的非线性系统更为一般,已知的系统信息更少:1)系统未知参数的范数的上界未知;2)具有关于可测输出非Lipschitz连续的非线性动态:3)系统输出显式地依赖于控制输入.通过设计自适应调节器来估计未知参数范数,从而给出了不基于未知参数先验信息的非线性自适应观测器设计的新方法.所设计的观测器为全局渐近收敛的,即实现了系统状态的渐近重构,确保了未知参数估计的一致有界性.此外,在系统输出不显式地依赖于控制输入的条件下,研究了降维观测器的设计问题.仿真例子验证了本文理论结果的正确性.     

Full-order observer design for linear systems with unknown inputs

In this article, a full-order observer without unknown inputs reconstruction is suggested in order to achieve finite-time reconstruction of the state vector for a class of linear systems with unknown inputs. The observer is a simple one, its derivation being direct and easy. It will be shown that the problem of full-order observers for linear systems with unknown inputs can be reduced in this case to a standard one (the unknown input vector will not interfere in the observer equations). The effectiveness of the suggested design algorithm is illustrated by a numerical example (aircraft longitudinal motion), and, for the same aircraft dynamics, we make a comparison between our new observer and other already existing observers from the existence conditions and dynamic characteristics’ point of view; the superiority of the new designed observer is demonstrated.     

A note on interval observer design for unknown input estimation

This paper addresses the problem of interval observer design for unknown input estimation in linear time-invariant systems. Although the problem of unknown input estimation has been widely studied in the literature, the design of joint state and unknown input observers has not been considered within a set-membership context. While conventional interval observers could be used to propagate with some additional conservatism, unknown inputs by considering them as disturbances, the proposed approach allows their estimation. Under the assumption that the measurement noise and the disturbances are bounded, lower and upper bounds for the unmeasured state and unknown inputs are computed. Numerical simulations are presented to show the efficiency of the proposed approach.     

未知输入和可测噪声重构之线性矩阵不等式非线性系统观测器设计

针对一类同时具有未知输入和输出可测噪声的Lipschitz非线性系统,讨论了状态估计、未知输入与可测噪声重构的问题.首先,基于广义系统和线性矩阵不等式的方法设计滑模未知输入观测器,不仅对原系统状态进行渐近估计,而且实现了对系统输出可测噪声的重构;其次,考虑一种鲁棒滑模微分器,实现了广义系统输出向量微分的精确估计,并在此基础上,提出了一种未知信息重构方法,该方法具有避免直接使用系统输出微分信息的优点.最后,对火车牵引拖动系统模型仿真,结果表明该方法不但能够实现对系统状态的估计,而且可以有效重构未知信息.     

Transformation of nonlinear discrete-time system into the extended observer form

The paper addresses the problem of transforming discrete-time single-input single-output nonlinear state equations into the extended observer form, which, besides the input and output, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of both the extended coordinate and output transformations, solving the problem, are formulated in terms of differential one-forms, associated with the input–output equation, corresponding to the state equations. An algorithm for transformation of state equations into the extended observer form is proposed and illustrated by an example. Moreover, the considered approach is compared with the method of dynamic observer error linearisation, which likewise is intended to enlarge the class of systems transformable into an observer form.     

基于分片线性函数逼近的非线性观测器设计

综合分片线性函数模型辨识/逼近和鲁棒观测器设计方法,研究了一大类非线性鲁棒观测器设计方法.所提出的算法能有效解决非线性系统的辨识/建模问题,并保证在一定的逼近精度下观测误差可以控制在一定的范围内,且观测误差随着逼近精度的提高而减小.