Interval observers for linear functions of state vectors of linear fractional‐order systems with delayed input and delayed output

This paper addresses the problem of interval observer design for linear functions of state vectors of linear fractional‐order systems, which are subjected to time delays in the measured output as well as the control input. By using the information of both the delayed output and input, we design two linear functional state observers to compute two estimates, an upper one and a lower one, which bound the unmeasured linear functions of state vectors. As a particular case with output delay only, we design a linear functional state observer to estimate (asymptotically) the unmeasured linear functions of state vectors. Existence conditions of such observers are provided, and some of them are translated into a linear programming problem, in which the observers' matrices can be effectively computed. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality, and effectiveness of the proposed design method.     

受扰非线性时滞系统近似最优跟踪控制

为了研究一类参考输入和扰动由外系统描述的非线性时滞系统最优输出跟踪问题,利用逐次逼近法将原最优跟踪问题转化为一族不含时滞项和超前项的非齐次线性两点边值问题序列,通过迭代求解该问题序列,提出了一个伴随向量解序列近似求解过程。最优输出跟踪控制律由解析的前馈-反馈项和以伴随向量的极限形式给出的非线性时滞补偿项组成,通过截取伴随向量序列的有限步迭代值,得到了问题的次优控制律。利用构造扰动和参考输入降维观测器,解决了前馈控制律的物理可实现问题;仿真结果表明,该方法计算量较小,容易工程实施,能有效地解决非线性时滞系统的最优跟踪控制问题。     

Hybrid adaptive observers for locally Lipschitz systems

An adaptive observer design approach is proposed for the class of nonlinear locally Lipschitz systems. The case of disturbances affecting the state equations is considered. The proposed solution is applicable to the systems with bounded solutions and hyperminimum phase linear part. It is based on the logic‐based control approach. Efficiency of the proposed observer design is demonstrated through computer simulations for Duffing and satellite system. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive observers for a class of multi-output non-linear systems

Sufficient differential geometric conditions are given for the existence of global adaptive observers for a class of multi-output non-linear systems which are linear with respect to a vector of unknown constant parameters. They extend to multi-output systems earlier results on adaptive observers for single-output systems; they also extend to systems with unknown parameters results obtained previously on the existence of non-adaptive observers with linear error dynamics.     

Adaptive finite‐time control for high‐order nonlinear systems with mismatched disturbances

In this paper, adaptive finite‐time control is addressed for a class of high‐order nonlinear systems with mismatched disturbances. An adaptive finite‐time controller is designed in which variable gains are adjusted to ensure finite‐time stabilization for the closed‐loop system. Chattering is reduced by a designed adaptive sliding mode observer which is also used to deal with the mismatched disturbances in finite time. The proposed adaptive finite‐time control method avoids calculating derivative repeatedly of traditional backstepping methods and reduces computational burden effectively. Three numerical examples are given to illustrate the effectiveness of the proposed method.     

具滞后的离散广义系统的无源控制

将无源的概念引入到滞后离散广义系统中，进而研究具滞后的离散广义系统在有界能量外部输入作用下的无源控制问题．基于广义Lyapunov函数，利用线性矩阵不等式和广义代数Riccati不等式，首先给出具滞后的离散广义系统E-渐近稳定且具有无源性的充分条件，然后在此基础上，得到存在状态反馈控制器，使得闭环系统E-渐近稳定且具有无源性的充分条件，并且由矩阵不等式的解给出相应的控制器构造方法。最后的数值算例说明了文中结论的有效性。     

不确定时滞组合系统基于状态观测器的鲁棒分散可靠控制

研究一类包含状态时滞和参数不确定性的不确定时滞组合系统基于状态观测器的鲁棒分散可靠控制问题。目的是设计分散状态观测器和基于此观测器的线见性动态输出反馈控制器，使得对于任意容许的不确定性以及在每一个子系统中预先指定执行器子集合内执行器的失效，相应的闭环系统渐近稳定。     

不确定组合时滞系统的鲁棒分散可靠控制

研究一类不确定组合时滞系统的状态反馈鲁棒分散可靠控制问题,系统包含状态时滞,非线性扰动和参数不确定性。目的是设计分散线性无记忆状态反馈控制器,使得对于任意容许的不确定性以及在每一个子系统中预先指定的执行器子集合内执行器的失效,相应的闭环系统渐近稳定。最后给出一个数值例子验证了本文所结结果的有效性。     

State estimation of system with bounded uncertain parameters: Interval multimodel approach

The objective of this study is the analysis of dynamic systems represented by a multimodel expression with variable parameters. Changes in these parameters are unknown but bounded. Since it is not possible to estimate these parameters over time, the simulation of such systems requires the consideration of all possible values taken by these parameters. More precisely, the goal is to determine, at any moment, the smallest set containing all the possible values of the state vector simultaneously compatible with the state equations and with a priori known bounds of the uncertain parameters. This set will be characterized by two trajectories corresponding to the lower and upper limits of the state at every moment. This characterization can be realized by a direct simulation of the system, given the bounds of its parameters. It can also be implemented with a Luenberger‐type observer, fed with the system measurements.     

Lurie型不确定时滞系统的时滞相关鲁棒绝对稳定性

针对一类具有范数有界不确定参数和未知常时滞的Lurie型不确定系统，建立了系统的时滞相关鲁棒绝对稳定性判据。所得结果表示为线性矩阵不等式(LMI)形式，应用MATLABLMI工具箱迭代求解可以得到时滞的上界，从而可对系统的允许时滞作出较高的估计。最后以一个例子说明其用法，并与现有文献比较以显示其有效性。     

线性时滞系统的鲁棒广义H2弹性控制

研究了系统被控对象存在不确定性,同时控制器也存在摄动的控制问题,采用Lyapunov稳定性理论和线性矩阵不等式(LMI)方法,以一组LMI形式给出了控制器存在的充分条件,并给出了弹性控制器的设计方法。仿真实例表明,该方法提高了时滞系统的广义H2控制的鲁棒性,验证了所提出方法的有效性。     

非线性时滞系统自适应神经网络Backstepping控制

针对一类未知非线性时滞系统,提出了一种自适应神经网络控制设计方案,将Backstepping、占有方法以及自适应界化技术结合起来构造了一个鲁棒自适应神经网络跟踪控制器,采用神经网络逼近未知时滞函数,放松了对非线性时滞函数的要求。通过构建一个恰当的Lyapunov-Krasoviskii泛函证明了闭环系统所有信号半全局一致最终有界,调节设计参数可以实现任意输出跟踪精确度。实例仿真说明了该方案的可行性。     

Adaptive IDA‐PBC for underactuated mechanical systems with constant disturbances

This work investigates the control of nonlinear underactuated mechanical systems with matched and unmatched constant disturbances. To this end, a new control strategy is proposed, which builds upon the interconnection‐and‐damping‐assignment passivity‐based control, augmenting it with an additional term for the purpose of disturbance compensation. In particular, the disturbances are estimated adaptively and then accounted for in the control law employing a new matching condition of algebraic nature. Stability conditions are discussed, and for comparison purposes, an alternative controller based on partial feedback linearization is presented. The effectiveness of the proposed approach is demonstrated with numerical simulations for three motivating examples: the inertia wheel pendulum, the disk‐on‐disk system, and the pendulum‐on‐cart system.     

一类离散时滞不确定系统的鲁棒控制

讨论了一类离散线性时滞不确定系统的鲁棒控制问题，利用Lyapunov方法，结合矩阵不等式性质，给出离散时滞系统对所有允许不确定性鲁棒稳定的充分条件，并设计出系统的状态反馈鲁棒控制器，所得结构分别基于相应的线性矩阵不等式（LMI）的解。     

改进的WPSS分段时延补偿方法

实现广域电力系统稳定器(WPSS)的工程应用的关键是对其反馈输入信号时延的良好补偿。对实际电网中相量测量单元(PMU)数据时延进行了实测,测试结果表明时延具有一定的随机分布特性和较强的抖动性。为适应时延的抖动特性,对分段时延补偿方法进行了改进,利用每次时延补偿器动作时刻前一段时间内的平均时延作为选择时延补偿的依据,避免了由于时延抖动带来的错误结果。在两区四机系统中进行的开环和闭环时频域仿真分析表明改进的方法能够更好地适应时延的变化,基于RTDS的实际电网仿真进一步验证了该方法在大系统中的有效性和可行性。     

Rejection of unknown periodic disturbances for continuous‐time MIMO systems with dynamic uncertainties

Rejection of unknown periodic disturbances in multi‐channel systems has several industrial applications that include aerospace, consumer electronics, and many other industries. This paper presents a design and analysis of an output‐feedback robust adaptive controller for multi‐input multi‐output continuous‐time systems in the presence of modeling errors and broadband output noise. The trade‐off between robust stability and performance improvement as well as practical design considerations for performance improvements are presented. It is demonstrated that proper shaping of the open‐loop plant singular values as well as over‐parameterizing the controller parametric model can significantly improve performance. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Design of impulsive adaptive observers for improvement of persistency of excitation

The development of adaptive observer techniques for nonlinear systems in the output canonical form is proposed applying additional impulsive feedback in the observer equations. The stability of new impulsive adaptive observer is investigated. It is shown that under some conditions, the proposed impulsive feedback can improve the rate of the observer convergence or relax the requirement on persistency of excitation, which is usually introduced to ensure convergence of the parameter estimates. The proposed feasibility conditions include positivity of dwell time (boundedness of impulse frequency) and solvability of some Lyapunov‐like matrix inequalities. The results are illustrated by simulation for three examples (including a single link flexible joint robot example). Copyright © 2014 John Wiley & Sons, Ltd.     

输入受限时滞系统的鲁棒模型预测控制

对于输入受限的不确定时滞系统，提出鲁棒模型预测控制方法。当预测状态在不变集之外时，采用双模控制结构，在固定的控制律上引入额外变量保证了输入可行性。为保证闭环系统稳定性，基于Lyapunov-Krasovskii函数构造了时滞系统特定的鲁棒不变椭圆集，并将椭圆集的设计转化为线性矩阵不等式的凸求解问题。该方法很多计算可以离线进行，从而减少了在线计算量。最后通过仿真验证了该方法的有效性。     

时变时滞不确定系统的鲁棒控制

基于二次稳定性理论,导出了时变时滞不确定系统鲁棒镇定的充分条件,应用ＬＭＩ方法,讨论了时变时滞不确定系统的鲁棒控制器设计问题,进而通过建立和求解不同的凸优化问题,给出了控制律满足不同指标要求的构造方法,最后给出一个算例,对该方法进行了验证。