一类不确定Lurie时滞奇异系统的鲁棒H∞控制

研究一类具有不确定性的Lurie时滞奇异系统的鲁棒稳定性分析和H∞状态反馈控制器设计方法.针对一类具有参数不确定性、未知时滞的奇异系统,得出了系统鲁棒稳定和鲁棒H∞状态反馈控制器存在的充分条件,它能使得不确定Lurie时滞奇异系统的解在所容许的范围内是正则的、无摄动的和稳定的;而且还得出了基于线性矩阵不等式(LMI)的鲁棒H∞状态反馈控制器的设计方法,使得闭环系统具有鲁棒稳定性和H∞性能.     

参数摄动系统的鲁棒LQ反馈控制

本文研究了不确定系统的鲁棒LQ反馈控制器的综合问题.对于具有线性有界实参数摄动的系统,首先把不确定系统的鲁棒LQ综合问题转化成N个确定系统的联立LQ综合问题.并据此提出了相应的综合算法.理论分析和实例计算结果表明所提出的方法具有较广的应用范围和较少的保守性.     

Lurie型控制系统的鲁棒决定稳定性

本文给出了Ｌｕｒｉｅ型间接控制系统ｘ＝Ｇ［Ｂ，Ｃ］ｘ＋Ｇ［Ｒ，Ｓ］ｆ（σ）；σ＝ｃ＾Ｔｘ－ρｆ（σ）；ｆ（σ）∈Ｋ［０，∞）；和直接控制系统ｘ＝Ｇ［Ｂ，Ｃ］ｘ＋Ｇ［Ｒ，Ｓ］ｆ（σ）；σ＝Ｃ＾Ｔｘ，ｆ（σ）∈Ｋ［０，∞），绝对稳定的若干充分条件。     

量化非线性控制——综述

量化控制系统设计通过将控制与通讯相结合来解决大量运用信息技术的现代工程系统的相关控制问题. 本文首先回顾近年来线性及非线性系统量化控制的结果. 其中, 非线性系统量化控制的发展尚处于初级阶段. 高维、量化、非线性及不确定性的共存导致量化非线性控制问题极具挑战性, 需要全新的思想和技术来解决. 本文重点回顾基于输入状态稳定性(ISS)及其回路小增益定理(Cyclic-small-gain theorem)的量化非线性控制设计方法, 同时列出该领域一些尚未解决的问题.     

非线性系统鲁棒耗散控制

基于二次型供给率,研究了不确定非线性系统的鲁棒耗散控制问题。不确定项用界范数来刻画。基于Hamilton-Jacobi不等式,得到了实现鲁棒耗散控制的充分条件及控制器的设计算法。     

一类模糊P I D 控制器的鲁棒优化设计

研究一类模糊 PID控制器的鲁棒设计。以小增益定理分析得到该模糊 PID控制系统稳定性条件。针对参数摄动系统的“最坏点”,用该稳定性条件作为约束 ,采用遗传算法对标称系统的性能进行优化 ,求得优化鲁棒控制器。以倒立摆为例进行鲁棒模糊 PID控制器的设计 ,实验结果表明了该方法的有效性     

Lurie滞后反馈控制系统绝对稳定的鲁棒扰动界

本文应用Lyapunov方法讨论了具有时滞反馈的 Lurie控制系统的鲁棒绝对稳定性,给出了具有一个和多个滞后反馈的Lurie控制系统的绝对 鲁棒稳定的充分条件．用本文的结论可直接计算具有时滞反馈的Lurie控制系统绝对稳定的 鲁棒扰动上界．文末给出了应用本文结论的例子．     

一类非线性系统的鲁棒H∞控制

研究一类可部分反馈线性化且具扰动三角结构的非线性参数不确定系统的鲁棒H∞控制问题,不确定参数属于已知紧集并以非线性形式进入系统.在输入到状态稳定的理论框架下,基于李雅谱诺夫函数和反演法构造出状态反馈控制器,使得闭环系统对所有允许的参数不确定性是内稳定的,且从扰动输入到输出有有界的L2-增益.控制器的设计不需解任何H am ilton-Jacob i方程,并给出仿真算例说明了该结论的可行性和有效性.     

不确定串联非线性系统H∞鲁棒自适应控制

针对一类含有未知参数和干扰的非最小相位串联非线性系统,结合H∞控制和自适应控制方法并利用李雅普诺夫函数递推设计方法设计了状态反馈H∞自适应控制器,避免了求解Hamilton-Jacobi-Isaacs不等式设计控制器的困难.该控制器不仅保证闭环系统ISS(input-to-state)稳定,而且使得系统对于所有允许的参数不确定从干扰输入到可控输出的 L 2增益不大于给定的值.最后,给出了一个仿真例子,仿真结果充分表明了所设计的控制器的可行性和有效性.     

基于回路成形的鲁棒增益调度控制器设计

针对目前基于线性变参数系统的增益调度控制设计中存在的控制结构复杂性问题，提出一种基于回路成形的简单且易实现的增益调度控制结构.在此基础上，提出一个鲁棒增益调度控制设计方法.设计过程首先采用补偿器函数使得被控对象奇异值具有期望的形状，以保证被控对象的性能要求，然后利用小增益定理设计一个鲁棒控制器，得到具有良好性能的、结构简单的鲁棒增益调度控制器.最后针对一个化工过程，说明此方法的有效性.     

随机时滞Lurie系统的鲁棒H∞和L2-L∞指数控制

针对一类具有范数有界不确定性和时变时滞的It^o型随机Lurie系统, 研究了鲁棒H_∞和L₂–L_∞指数控制问题. 利用Lyapunov-Krasovskii泛函方法和It^o微分公式, 得到了以线性矩阵不等式(LMIs)表示的控制器存在的充分条件. 对所有容许的参数不确定性, 设计的无记忆状态反馈控制器使闭环系统鲁棒指数均方稳定, 且具有给定的H_∞和L₂–L_∞干扰抑制度. 最后, 通过两个仿真例子说明了所提方法的有效性.     

Robust absolute stability of Lurie interval control systems

This paper considers robust absolute stability of Lurie control systems. Particular attention is given to the systems with parameters having uncertain, but bounded values. Such so‐called Lurie interval control systems have wide applications in practice. In this paper, a number of sufficient and necessary conditions are derived by using the theories of Hurwitz matrix, M matrix and partial variable absolute stability. Moreover, several algebraic sufficient and necessary conditions are provided for the robust absolute stability of Lurie interval control systems. These algebraic conditions are easy to be verified and convenient to be used in applications. Three mathematical examples and a practical engineering problem are presented to show the applicability of theoretical results. Numerical simulation results are also given to verify the analytical predictions. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust quantized output feedback control for uncertain discrete time‐delay systems with saturation nonlinearity

This paper is concerned with robust quantized output feedback control problems for uncertain discrete‐time systems with time‐varying delay and saturation nonlinearity. It is assumed that the quantizer is of the saturating type. A new framework for the local boundedness stabilization of quantized feedback systems is developed. Attention is focused on finding a quantized static output feedback controller such that all trajectories of the resulting closed‐loop system starting from an admissible initial basin converge to a bounded region strictly within the initial basin. A quantized feedback controller is proposed, which comprises output feedback and the exogenous signal parts. Simulation examples are given to illustrate the effectiveness and advantage of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Lurie网络化控制系统的保性能控制

以不确定Lurie系统作为被控对象,研究其在网络环境下的保性能控制问题.在同时考虑随机网络诱导时延和数据丢包的情况下,建立不确定Lurie网络化控制系统模型;利用Lyapunov方法分别给出了存在结构不确定性和范数有界的不确定性时,Lurie网络化控制系统保性能控制器的设计方法.所得结果是以线性矩阵不等式的形式给出的,便于数值求解.最后以数值实例说明了所提出方法的可行性和有效性.     

Robust adaptive fault‐tolerant quantized control of nonlinear systems with constraints on system behaviors and states

In this work, we develop a robust adaptive fault‐tolerant tracking control scheme for a class of input‐quantized strict‐feedback nonlinear systems in the presence of error/state constraints and actuation faults. The problem is rather complicated yet challenging if nonparametric uncertainties and unknown quantization parameters as well as time‐varying yet completely undetectable actuation faults are involved in the considered systems. Compared with the most existing approaches in the literature, the proposed control exhibits several attractive advantages: (1) upon using a nonlinear decomposition for quantized input and employing the robust technique for actuation fault, not only the exact knowledge of quantization parameters are not required, but also the actuation fault can be easily compensated since neither fault detection and diagnosis/fault detection and identification nor controller reconfiguration is needed; (2) based on the error/state‐dependent unified nonlinear function, the constraints on tracking error and system states are directly handled and the cases with or without constraints can also be addressed in a unified manner without changing the control structure; and (3) the utilization of unified nonlinear function‐based dynamic surface control not only avoids the problem of the explosion of complexity in traditional backstepping design, but also bypasses the demanding feasibility conditions of virtual controllers. Furthermore, by using the Lyapunov analysis, it is ensured that all signals in the closed‐loop systems are uniformly ultimately bounded. The effectiveness of the developed control algorithm is confirmed by numerical simulations.     

Structurally variable control of time-varying Lurie systems

This poses and solves the problem of structurally variable control synthesis for time-varying Lurie systems, which has both theoretical and engineering significance. A theorem on absolute stability of a set related to Lurie systems solves the problem. The theorem is basic for proving control algorithms that ensure absolute stability of a sliding subspace or its stability with finite reachability time. Moreover, they ensure the attraction in the whole of the zero equilibrium state of the whole control system of the plant on N(L). The selection of the sliding subspace can be such that the system nonlinearity does not influence the sliding motion.     

多时滞Lurie控制系统的时滞相关鲁棒稳定性

时滞Lurie控制系统的稳定性条件与Lyapunov函数的选取有关.本文对多时滞Lurie控制系统进行了变换,然后选择一个适当的Lyapunov函数,利用Lyapunov稳定性方法并结合Moon引理,得到了多时滞Lurie控制系统的时滞相关鲁棒稳定性判别条件,该条件是以线性矩阵不等式(LMI)给出的,可用Matlab求解.最后用一个算例验证了所得方法的有效性.     

Absolute stability of Lurie networked control systems

This paper is concerned with the absolute stability problem of networked control systems (NCSs) with the controlled plant being Lurie systems (Lurie NCSs), in which the network‐induced delays are assumed to be time‐varying and bounded. First, in consideration of both the time‐varying network‐induced delays and data packet dropouts, the Lurie NCSs can be modeled as a multiple‐delays Lurie system. Then, a delay‐dependent absolute stability condition is established by using the Lyapunov–Krasovskii method. Next, two approaches to controller design are proposed in the terms of simple algebra criteria, which are easily solved via the toolbox in Matlab. Furthermore, the main results can be extended to robust absolute stability of Lurie NCSs with the structured uncertainties, where robust absolute stability conditions and approaches to robust controller design are presented. Finally, two numerical examples are worked out to illustrate the feasibility and the effectiveness of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust adaptive output feedback control for uncertain nonlinear systems with quantized input

In this paper, we study the input quantization problem for a class of uncertain nonlinear systems. The quantizer adopted belongs to a class of sector‐bounded quantizers, which basically include all the currently available static quantizers. Different from the existing results, the quantized input signal, rather than the input signal itself, is used to design the state observers, which guarantees that the state estimation errors will eventually converge to zero. Because the resulting system may be discontinuous and non‐smooth, the existence of the solution in the classical sense is not guaranteed. To cope with this problem, we utilize the non‐smooth analysis techniques and consider the Filippov solutions. A robust way based on the sector bound property of the quantizers is used to handle the quantization errors such that certain restrictive conditions in the existing results are removed and the problem of output feedback control with input signal quantized by logarithmic (or hysteresis) quantizers is solved for the first time. The designed controller guarantees that all the closed‐loop signals are globally bounded and the tracking error exponentially converges towards a small region around zero, which is adjustable. Copyright © 2016 John Wiley & Sons, Ltd.     

一类Lurie 时滞广义系统的时滞相关H∞ 控制

研究一类Lurie时滞广义系统的H∞控制问题.以矩阵不等式形式给出了保证闭环系统正则、无脉冲、全局一致渐近稳定且具有给定性能的时滞相关充分条件.进一步,以非凸约束下的线性矩阵不等式(LMIs)的可行解给出了状态反馈控制律设计方法.仿真算例表明了所提出方法的有效性.