基于辅助输出的线性系统状态和未知输入同时估计方法

在未知输入观测器匹配条件不满足的情况下, 针对一类线性时不变系统, 研究了同时估计系统 状态和未知输入的问题. 首先, 基于可测输出对未知输入的相关度的概念, 给出了辅助输出 的构造方法, 使得匹配条件得以满足. 为了处理辅助输出中的未知信息, 提出了一种高增益 观测器设计方法, 它不仅能估计辅助输出, 而且还能估计辅助输出的导数. 然后, 基于辅助 输出的估计值, 提出了一种降维观测器设计方法, 可以在不受未知输入影响的情况下估计系统 的状态; 接下来, 基于状态和辅助输出及其导数的估计值, 给出了未知输入估计. 最后, 对一个五 阶系统进行了数字仿真, 仿真结果表明所提出的方法是有效的.     

状态估计与未知输入和可测噪声同时重构方法

针对一类不确定线性系统,讨论了状态估计及未知输入和可测噪声重构方法。首先,对仅具有未知输入的线性系统,讨论了观测器匹配条件不满足前提下的状态估计和未知输入重构问题;通过设计降维观测器和高阶滑模观测器,提出一种未知输入代数重构方法;然后,将以上结论上升到具有未知输入和可测噪声的线性系统,以此提出了状态估计及未知输入和可测噪声同时重构的方法;最后,通过对飞行器模型进行仿真,验证了所提出方法的有效性。     

一类不确定切换中立型系统的鲁棒滑模控制

针对一类不确定切换中立型系统, 设计相应的积分型滑模面. 基于平均驻留时间方法和线性矩阵不等式技术, 给出滑模动力学系统鲁棒指数渐近稳定的时滞相关性判据. 通过设计滑模控制器, 使闭环系统的状态满足到达条件. 数值仿真表明, 所提出的方法是有效可行的.

     

一类不受控离散事件驱动不确定线性切换系统优化控制

考虑一类不受控离散事件驱动不确定约束线性切换系统, 提出具有任意切换特性的约束优化控制策略. 引入有限时域性能函数, 定义约束最优控制问题. 为降低控制器的在线计算量, 通过参数化方法压缩最优控制问题决策变量的维数. 应用公共Lyapunov 函数和控制Lyapunov 函数理论建立的闭环切换系统, 具有对不确定扰动和不受控切换信号的渐近稳定性和逆最优性. 最后通过算例仿真验证了结果的有效性.

     

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.     

带有乘性过程噪声和模式观测时滞离散马氏跳线性系统的状态估计

研究受乘性过程噪声干扰的离散马氏跳线性系统状态估计问题. 系统可得到的观测包括两部分: 模式观测和输出观测, 其中模式观测受到固定时滞的影响. 利用贝叶斯定理及所得到的一些结果, 提出一种新颖的最小均方误差意义下次优状态估计算法. 该次优算法是回归的, 并且不随着时间增加而加重计算存储负荷. 通过计算机仿真来评估所提出次优算法的性能, 仿真结果验证了该算法的优越性.

     

基于H_/H∞未知输入观测器的线性切换系统故障检测

利用H_/H_∞未知输入观测器方法研究线性切换系统的故障检测问题.将未知输入干扰分解为可解耦和不可解耦两部分,从估计误差中消除可解耦部分,再使用加权H_/H_∞混合性能指标表示剩余未知输入和故障对残差的影响,将故障检测问题等价为加权H_/H_∞未知输入观测器设计问题.根据平均驻留时间技术和多Lyapunov函数方法设计了故障检测器参数,并利用松弛矩阵方法得到了进一步的结果.通过一个仿真例子对所提出方法进行了验证.     

基于高阶滑模观测器的状态和未知输入同时估计方法

对一类含有未知输入的仿射非线性系统,讨论了一种能同时估计系统状态和末知输入的未知输入观测器设计方法.首先利用李导数对仿射非线性系统进行线性化,将其转化为可控标准型.其次,针对变化后的等价系统,提出了一种高阶、高增益滑模观测器,由此不仅能得到系统状态的估计,同时还得到状态微分的估计.再次,基于状态及其微分的估计,对未知输入提出了一种重构方法.该方法能对强时变未知输入重构,而且重构中没有用到系统微分的信息.最后,通过对两个实际模型的仿真,表明了方法的可行性.     

含未知输入的广义系统的状态与输入估计

研究了含未知输入的广义系统的输入解耦观测器设计问题. 在系统脉冲能控的条件下通过系统输入-状态对的非奇异变换, 把此问题等价地转化为正常状态空间系统的相应问题. 用大家熟知的方法设计正常状态空间系统的观测器, 从而得到广义系统的输入解耦观测器. 然后用广义系统的观测器状态和系统输出的线性组合渐近估计系统的状态与未知输入.     

同时含有未知输入和测量干扰系统全维和降维观测器设计

针对同时含有未知输入和测量干扰的不确定系统研究了全维和降维观测器设计问题. 首先, 利用待定系数法给出了全维观测器的结构和存在条件. 该条件完全由原系统的系统矩阵给出, 易于检验. 对于降维观测器, 为了消除测量干扰的影响, 提出了一种新的测量输出构造方法, 使得新构造的测量输出不再包含干扰信号. 此外, 证明了全维和降维观测器存在条件的内在统一性, 即全维观测器所需要满足的观测器匹配条件和强可检测条件在研究降维观测器所要讨论的新的系统中都可以得到保持. 因而, 在全维观测器存在条件下, 也可以设计一个相应的降维观测器. 最后, 给出了一个数值例子验证所提方法的有效性.     

Simultaneous state and output disturbance estimations for a class of switched linear systems with unknown inputs

The paper considers the issues of state estimation and output disturbance reconstruction for a class of switched linear systems with unknown inputs. A singular switched system is derived from the original switched system by taking the output disturbance as a part of a new extended state vector. For the constructed singular switched system, a robust sliding-mode switched observer which can not only estimate the states of original switched system but also reconstruct output disturbances is proposed, where the switching of the observer is synchronous with that of the switched system. A sufficient condition is provided to guarantee the existence of the switched observer by the feasibility of an optimisation problem with linear matrix inequality constraint, and the corresponding switching signal with average dwell time is designed such that the convergence of the estimation error system is proven to be exponential. Based on the state estimation of singular switched system, the methods of state estimation and output disturbance reconstruction of original switched system are proposed. Finally, the simulation results confirm the predicted performance of the proposed methods.     

连续线性切换系统的镇定慢切换设计

针对含有两个不稳定子系统的线性切换系统,设计一种包含时间驱动和状态驱动两个环节的切换法则,使线性切换系统稳定.在该切换法则下,系统的类Lyapunov函数在两个环节都不需要严格单调递减,使得系统在每个子系统有更长的驻留时间,从而有效降低系统的切换频率.在适当的假设条件下,带时变扰动的线性切换系统在该切换信号下具有良好的鲁棒稳定性.基于此,当系统可观测时,进一步设计了基于观测器的混合切换法则,实现了系统的鲁棒稳定.     

离散Lipschitz非线性系统状态和未知输入估计

针对含有未知输入和可测噪声的离散Lipschitz非线性系统,研究了状态估计、未知输入以及可测噪声同时估计的问题.首先,对含有未知输入的系统,设计了比例积分观测器,达到同时估计系统状态和未知输入之目的.分析了残差系统的观测性和稳定性,利用H_∞实现该观测器对时变未知输入的有效估计;其次,将观测器增益矩阵的求解转化为求解线性矩阵不等式的形式;进一步地,基于系统状态扩展方法,将所提方法推广至同时含有未知输入和可测噪声的系统;最后,通过两个仿真算例说明了所提方法的正确性和有效性.     

Control of switched linear systems with input saturation

The problem of control of switched linear systems with input saturation is considered. A synthesis method based on the minimum dwell time switching together with saturated feedbacks is presented. Sufficient conditions for stability are proposed in term of linear matrix inequalities. An illustrative example is presented to show the validity of the results.     

State and input simultaneous estimation for discrete‐time switched singular delay systems with missing measurements

This paper presents an approach to simultaneously estimating the states and inputs of discrete‐time linear switched singular state‐delayed systems with unknown inputs, multiple missing measurements, and average dwell time (ADT) switching. In each output measurement channel of the system, the data loss incident is controlled by an individual stochastic variable obeying a certain probability distribution on the interval [01]. The proposed approach is based on the design of a switched, loss‐probability‐dependent proportional integral observer under the ? ₂ input attenuation framework. By using piecewise Lyapunov function technique, ADT scheme, stochastic analysis, and projection lemma, sufficient conditions for the existence of such an observer are established in terms of linear matrix inequalities, which guarantee that the resulting estimation error system is stochastically exponentially admissible and achieves an (non‐weighted) ? ₂ gain from the augmented unknown input to the state and unknown input estimation errors under ADT switching. Moreover, a method is provided to seek the minimum allowable ? ₂ gain level for a desired ADT of the switching signals. The effectiveness of the proposed approach is illustrated by a simulation example of direct current (DC) servomechanism control system. Copyright © 2016 John Wiley & Sons, Ltd.     

Multiple sliding mode observers and unknown input estimations for Lipschitz nonlinear systems

Multiple sliding mode observers for state and unknown input estimations of a class of MIMO nonlinear systems are systematically developed in this paper. A new nonlinear transformation is formulated to divide the original system into two interconnected subsystems. The unknown inputs are assumed to be bounded and not necessarily Lipschitz, and do not require any matching condition. Under structural assumptions for the unknown input distribution matrix, the sliding mode terms of the nonlinear observer are designed to track their respective unknown inputs. Also, the unknown inputs can be reconstructed from the multiple sliding mode structurally. The conditions for asymptotic stability of estimation error dynamics are derived. Finally, simulation results are given to demonstrate the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Stability analysis of switched positive linear systems with stable and unstable subsystems

This paper addresses the stability problem of switched positive linear systems with stable and unstable subsystems. Based on a multiple linear copositive Lyapunov function, and by using the average dwell time approach, some sufficient stability criteria of global uniform exponential stability are established in both the continuous-time and the discrete-time cases, respectively. Finally, some numerical examples are given to show the effectiveness of the proposed results.