不确定非线性系统的鲁棒稳定性分析

基于泛函分析和算子理论的方法,从输入输出的角度研究了一类不确定反馈非线性系统的鲁棒稳定性问题.利用K类函数分别描述非线性不确定环节和非线性系统的算子增益,对非线性反馈互联不确定系统的鲁棒稳定性问题进行了研究.接着利用小增益条件的形式进行等价变化,就可将反馈不确定非线性系统的稳定性条件转化成系统非线性算子的范数条件.并通过举例证明了该方法的有效性.     

针对一类非线性系统的多变量线性 扩张状态观测器及其收敛性分析

针对一类非线性不确定系统,构造了一种多变量线性扩张状态观测器（Multi-variable linear extended state observer,MVLESO）,用于实时估计非线性系统的不确定动态.采用频域分析方法,剖析了所构造的MVLESO在非线性系统不确定动态估计方面的收敛性,并推导出不确定动态的频域估计误差模型.仿真结果表明,所设计的MVLESO可以较为精准地估计出非线性系统当前的不确定动态,该特性为基于MVLESO鲁棒控制方案的有效实施奠定了基础.     

基于MME非线性系统递推辨识算法改进及仿真

该文介绍了最小模型误差估计算法（MME）和在非线性不确定系统辨识中的应用,以及分析了基于此算法的系统的鲁棒性的几个方面。并且,基于最优化理论控制以及两点边值问题,采用不变式嵌入法,给出了模型不确定非线性系统中基于MME在线递推估计算法,并首次提出了在满足协方差约束的前提下,如何最优地选择正定矩阵W的初值,以使非线性不确定系统的辨识结果达到最佳。最后,基于此算法,给出了非线性离散系统的仿真实例,仿真结果说明,最优地选择W的初值,使该方法是模型不确定非线性系统中辨识的有效方法。     

船舶动力定位非线性自适应反步控制器设计

针对扰动不确定非线性船舶动力定位问题,提出了一种带观测器的不确定扰动非线性船舶动力定位自适应输出反馈控制.设计了一个非线性观测器,从附有噪声的输出中估计出船舶位置以及运动速度.用滤波后的位置信号,针对扰动不确定非线性船舶设计带观测器的自适应反步控制器,该控制在Backstepping设计方法的基础上引入积分环节,对存在未知参数和动态不确定扰动的船舶能有效的改善系统性能.根据Lyapunov稳定性理论证明所设计的控制器是全局渐近稳定的,仿真结果验证了该方法的有效性.     

一类非线性组合大系统的分散输出反馈鲁棒镇定1)

研究了不确定非线性子系统经不确定非线性互联而成的组合大系统,给出了其可分散输出反馈鲁棒镇定的充分条件,说明了所得结论的广泛适用性以及相似结构与全息特性的密切相关性.     

基于非线性参数神经网络的非线性系统稳定自适应控制

针对不确定仿射非线性系统,提出一种基于非 线性参数神经网络的稳定自适应控制方案,在非线性参数神经网络对不确定非线性函数的逼 近误差的界未知的情形下,对网络逼近误差界进行在线自适应估计,并由Lyapunov理论证明 了整个闭环控制系统的稳定性．     

非线性不确定系统鲁棒镇定的H~∞方法

考虑了仿射非线性不确定系统的鲁棒镇定性。在不确定项为有界结构下将系统化为一个确定的标称系统Ｈ∞问题来考虑，利用非线性系统Ｈ∞控制理论的现有结论讨论系统的鲁棒性。首次将非线性Ｈ∞控制理论方法引入到一般仿射非线性系统的鲁棒性讨论中。最后给出一个例子说明此方法的适用性。     

不确定非线性环链系统的分散鲁棒控制

提出了环链系统和一类不确定非线性环链系统,利用线性代数理论,给出了实现环链系统的充要条件,运用李雅普诺夫稳定理论和矩阵理论研究了不确定非线性环链系统的鲁棒镇定,并给出了一种非线性鲁棒镇定控制器的设计,还考虑了一类非线性环链相似组合大系统,给出了分散鲁棒镇定条件,最后给出数值例子说明设计方法的有效性。     

带有非线性不确定奇异系统的积分滑模控制

针对一类含有非线性不确定的奇异系统, 提出了一种面向性能的鲁棒控制器. 控制器由3部分组成: 积分滑模控制、附加的非线性控制及复合非线性反馈控制. 积分滑模控制可将匹配不确定完全抵消并使系统轨迹进入理想滑模; 附加的非线性控制用来抑制理想滑动模态上非匹配不确定对系统稳定性和性能的影响; 复合非线性反馈控制则保证闭环系统输出按性能要求渐近地跟踪参考输入信号. 最后通过算例说明所提算法的有效性.     

非线性不确定系统的鲁棒性研究

1　引言非线性不确定系统的鲁棒性研究 ,早期是以在匹配条件 (matching condition)和广义匹配条件下 ,设计控制器使闭环系统达到实际稳定 (practical stabitity)为主 [1～ 3 ] .近些年利用 H∞ 控制理论的结果 ,出现了对具有有界结构的非线性不确定系统的鲁棒性讨论 [4～ 9] .模有界结构条件下 ,非线性不确定系统的鲁棒性有可能达到使状态趋于平衡点 ,而非仅仅实际稳定 .在文献 [4]中所讨论的非线性系统 ,要求其非线性部分具有线性界 .文献 [5 ]首次将模有界结构条件引入到线性不确定系统的鲁棒性研究中 .文献 [6]进一步讨论了这一结构下的…     

On the quasi-balanceable class of linear quantum stochastic systems

This paper is concerned with the characterization of the quasi-balanceable class of linear quantum stochastic systems (i.e., systems that can be approximated via the recently proposed quasi-balanced truncation method). It has previously been shown that the quasi-balanceable class of systems includes the class of completely passive systems. In this work, we refine the previously established characterization of quasi-balanceable systems and show that the class of quasi-balanceable systems is strictly larger than the class of completely passive systems. We derive a novel characterization of completely passive linear quantum stochastic systems solely in terms of the controllability Gramian of such systems. Exploiting this result, we prove that all linear quantum stochastic systems with a pure Gaussian steady state (active systems included) are all quasi-balanceable, and establish a new complete parameterization for this important class of systems. Examples are provided to illustrate our results.     

Feedback transformation of linear systems

In this paper we define a feedback transformation as an operation on a class of linear systems and investigate its properties within the framework of the mathematical theory of general systems. In particular, the class of linear systems produced from an arbitrary fixed linear system by the feedback transformation is characterized. Furthermore, a decoupling condition for linear systems is presented as well as a relation between the class of linear systems that can be decoupled and the class of invertible linear systems.     

Design of switched controllers for discrete singular bilinear systems

In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems.The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.     

Design of switched controllers for discrete singular bilinear systems

In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems.The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.     

Pseudo‐energy shaping for the stabilization of a class of second‐order systems

A Lyapunov direct method is presented for a class of second‐order systems that includes mechanical systems. This method shall be called a pseudo‐energy shaping method because it reduces to the energy shaping method when a given second‐order system is a mechanical system. The pseudo‐energy shaping method comprehends both the Lyapunov direct method for mechanical systems proposed by Aguilar‐Ibañez and the controlled Lagrangian method that has been successfully applied to stabilize mechanical systems. A class of second‐order systems including mechanical systems is defined first. For this class, matching conditions are derived for the construction of an energy‐like Lyapunov function that shall be called a pseudo‐energy function. Easily verifiable conditions are then presented for stabilizability by the pseudo‐energy shaping method for a class of second‐order linear systems and for a class of second‐order nonlinear systems with one degree of under‐actuation. These results are applied to stabilize a two‐dimensional overhead crane system and a three‐link robot arm system. Copyright © 2011 John Wiley & Sons, Ltd.     

On modularity in infinitary term rewriting

We study modular properties in strongly convergent infinitary term rewriting. In particular, we show that:

• •Confluence is not preserved across direct sum of a finite number of systems, even when these are non-collapsing.
• •Confluence modulo equality of hypercollapsing subterms is not preserved across direct sum of a finite number of systems.
• •Normalization is not preserved across direct sum of an infinite number of left-linear systems.
• •Unique normalization with respect to reduction is not preserved across direct sum of a finite number of left-linear systems.

Together, these facts constitute a radical departure from the situation in finitary term rewriting. Positive results are:

• •Confluence is preserved under the direct sum of an infinite number of left-linear systems iff at most one system contains a collapsing rule.
• •Confluence is preserved under the direct sum of a finite number of non-collapsing systems if only terms of finite rank are considered.
• •Top-termination is preserved under the direct sum of a finite number of left-linear systems.
• •Normalization is preserved under the direct sum of a finite number of left-linear systems.

All of the negative results above hold in the setting of weakly convergent rewriting as well, as do the positive results concerning modularity of top-termination and normalization for left-linear systems.     

Exponential stability of a class of nonlinear dynamical systems with uncertainties

Exponential stability for a class of nonlinear dynamical systems with uncertainties is investigated. Based on the stability of the nominal systems, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such a class of feedback controllers, we can guarantee exponential stability of uncertain nonlinear dynamical systems. Our approach can give a clear insight into system analysis. Finally, an illustrative example is given to demonstrate the utilization of the approach developed in this paper.     

Global asymptotic stabilisation of non-linear systems

In this article, the problem of global asymptotic stabilisation of non-linear systems is considered. First of all, the global asymptotic stability of a class of non-linear systems is considered. It is proved that the class of non-linear systems is globally asymptotically stable under certain appropriate conditions. Secondly, based on the result obtained, the global asymptotic stabilisation of a class of non-linear systems is investigated, and the feedback control laws, which globally stabilise the class of systems, are designed. Thirdly, by the coordinate change and the results obtained, the global stabilisation of the affine non-linear systems are studied, and then some sufficient conditions of stabilisation are presented. Finally, the global asymptotic stabilisation of partially linear cascade non-linear system is considered. The sufficient conditions of global stabilisation are obtained, and the corresponding feedback control laws, which stabilise the non-linear systems, are designed. In addition, some examples are given to show the effectiveness of the new results.     

非线性系统控制的逆系统方法(I)——单变量控制理论

介绍非线性系统控制的逆系统方法及相应的单变量非线性系统的控制理论。包括:逆系统方法的基本概念和设计原理,单变量系统α阶积分逆的设计方法,连续单变量系统的控制,逆系统方法在一类分布参数系统和离散时间系统上的推广示例。