基于神经网络的非线性系统近似线性化

神经网络具有同时逼近某一函数及其高阶导数的功能，这一结果为神经网络在非线性系统中的应用提供了可行的工具，本文提出了一种利用网络的近似功能的非线性系统的近似线性方法，无论系统是否满足可积条件，神经网络都可实现其对各条件的近似职分，从而构造满足系统近似线性化的反馈控制，对球－杆系统的仿真结果显示了这种方法的有效性。     

神经网络广义逆系统控制

提出适合于高阶非线性系统线性化解耦的广义逆系统，它与被控系统复合后，不但能实现原系统的线性化和解耦，而且通过合理地设计逆系统，可使伪线性复合系统的极点在复平面上任意配置，进一步提出由静态神经网络和若干积分惯性等线性环节组成的神经网络广义逆系统，为模型未知且内部状态不易测量的高阶非线性系统的线性化解耦控制提供一条有效途径，进一步拓展了神经网络逆系统控制方法的适用范围。     

多关节机器人的一种非线性反馈控制方法

本文研究了一种基于高阶线性化近似方法的机器人非线性反馈控制问题。首先,给出了多关节机器人的动力学模型,研究了一般非线性系统相对于某一标称轨迹的高阶线性近似方法,建立了高阶反馈项系数的计算公式,然后,讨论了多关节机器人的二阶近似非线性反馈控制方案。最后,给出了数字仿真结果.     

基于反馈线性化系统的非线性鲁棒控制μ方法

对于可状态反馈线性化的一类仿射非线性系统，本文提出一种非线性鲁棒控制的μ方法。首先给出非线性鲁棒控制问题，然后利用状态反馈线性化方法，把非线性系统线性化，并利用μ综合方法，对线性化系统进行鲁棒控制器的设计，最后通过回代构成非线性鲁棒控制系统。     

非线性倒立摆起摆和稳定控制研究

该文深入研究了直线倒立摆的摆起和稳定控制。通过两种方法对倒立摆非线性模型进行线性化得到线性化模型。第一种方法是利用微分几何李导数理论，对坐标和输入输出进行变换，然后在局部进行线性化得到一个线性化模型；另一种方法直接在平衡点附近进行线性化得到线性化模型。最后用MATLAB仿真和实物控制分别证明了能量反馈理论和稳定控制理论具有良好的控制效果，且通过Lie理论对系统进行坐标变换得到线性化模型比略去高阶项得到的线性化模型具有更好的鲁棒性和控制效果。     

非线性系统完全线性化方法的研究

本文针对非线性系统，运用微分几何理论，提出了一种基于完全线性化的控制方法。同时还给出了这种非线性系统线性化的条件和状态变换的构造方法，将这种控制方案应用在聚合反应过程中，仿真结果表明它具有良好的跟踪能力以及较好的参数鲁棒性。     

神经网络广义逆系统控制

提出适合于高阶非线性系统线性化解耦的广义逆系统.它与被控系统复合后,不但能实现原系统的线性化和解耦,而且通过合理地设计逆系统,可使伪线性复合系统的极点在复平面上任意配置.进一步提出由静态神经网络和若干积分惯性等线性环节组成的神经网络广义逆系统,为模型未知且内部状态不易测量的高阶非线性系统的线性化解耦控制提供一条有效途径,进一步拓展了神经网络逆系统控制方法的适用范围.     

离散非线性解耦控制算法及其在长形电阻炉中的应用

本文针对一类离散非线性系统，提出了一种输入／输出解耦线性化控制算法。并针对一工业无纺针热处理长形电阻炉，通过系统辩识的方法得到离散非线住系统模型，并将所开发的非线性解耦控制算法应用于该电阻炉。工业应用结果表明，利用非线性控制算法可以较好地解决工业电加热炉的控制。     

一类非线性参数化系统白适应重复学习控制

针对一类高阶非线性参数化系统,利用分段积分机制,提出了一种新的自适应重复学习控制方法．该方法结合反馈线性化,可以处理参数在一个未知紧集内周期性快时变的非线性系统,通过引进微分一差分混合型参数自适应律,设计了一种自适应控制策略,使广义跟踪误差在误差平方范数意义下渐近收敛于零,通过构造Lyapunov泛函,给出闭环系统收敛的一个充分条件．实例仿真结果说明了该方法的可行性．     

高阶系统方法— I.全驱系统与参数化设计

本文首先指出了控制领域中普遍使用的增广一阶系统方法的弊端, 介绍了高阶全驱系统的概念及其在控制器设计方面的优势, 并通过一些基础物理定律、串联系统、严反馈系统和可反馈线性化系统等例子说明了高阶全驱系统的普遍性, 进而指出高阶全驱系统是动态系统的一种描述形式, 是面向控制的模型.然后介绍了一类高阶全驱系统的一种参数化设计方法.通过适当选取一类非线性状态反馈控制律, 可获得一个具有希望特征结构的线性定常闭环系统, 并给出了闭环系统特征向量和反馈控制律的完全参数化表示, 讨论了解的存在性条件以及设计参数集合的稠密性等相关问题.最后对高阶全驱系统方法的后续问题做了说明和展望.     

Linearization and state estimation of unknown discrete-timenonlinear dynamic systems using recurrent neurofuzzy networks

Model-based methods for the state estimation and control of linear systems have been well developed and widely applied. In practice, the underlying systems are often unknown and nonlinear. Therefore, data based model identification and associated linearization techniques are very important. Local linearization and feedback linearization have drawn considerable attention in recent years. In this paper, linearization techniques using neural networks are reviewed, together with theoretical difficulties associated with the application of feedback linearization. A recurrent neurofuzzy network with an analysis of variance (ANOVA) decomposition structure and its learning algorithm are proposed for linearizing unknown discrete-time nonlinear dynamic systems. It can be viewed as a method for approximate feedback linearization, as such it enlarges the class of nonlinear systems that can be feedback linearized using neural networks. Applications of this new method to state estimation are investigated with realistic simulation examples, which shows that the new method has useful practical properties such as model parametric parsimony and learning convergence, and is effective in dealing with complex unknown nonlinear systems.     

Cascaded feedback linearization and its application to stabilization of nonholonomic systems

In this paper, a new cascaded feedback linearization problem is formulated and a set of conditions on the cascaded feedback linearizability are established for a class of two-input affine nonlinear systems. The proposed cascaded feedback linearization method enlarges the classes of nonlinear systems which can be dealt with using the feedback linearization technique. In particular, the proposed design can be applied to address the feedback stabilization problem for a few classes of nonlinear systems which have uncontrollable linearization and do not satisfy the standard feedback linearization conditions. As an illustrative application, the proposed cascade feedback linearization concept is used to solve the feedback stabilization problem of nonholonomic systems within the framework of continuously differentiable state feedback control. Simulation results are provided to illustrate the proposed method.     

Successive linearizations of second order multidimensional time-invariant systems

The present paper discusses a linearization method for second order multidimensional time-invariant systems. The method approximates locally the nonlinear vector field around the equilibrium, where the solution starting from a given initial state near the equilibrium is approximated by a linear solution. This linearization is usually called local trajectory-based linearization. The approximation is computed using an iterative method, which consists of successive approximations in the least square sense. Using a numerical example, it is shown that the linearized solutions exhibit good agreement with the nonlinear solutions.     

Transformation of a nonlinear system into an augmented linear system

This paper presents a method of formal linearization by augmenting state variables for nonlinear systems. Introducing a sequence of linearly independent functions and regarding each of them as a new state variable, the original nonlinear system is transformed into an augmented linear system. Based on this linearization, the paper also derives an observer and a suboptimal controller for nonlinear systems. The examples indicate that the linearization has excellent characteristics and greatly improves the performances.     

非线性大系统的分散线性化与分散控制

将非线性控制系统的精确线性化方法应用于非线性大系统,提出了非线性大系统 的分散线性化方法,并得到了非线性系统可分散线性化的充要条件.按照这个方法,可将难度 较大的一类非线性大系统分散控制器的设计转化为易于处理的线性大系统分散控制器的设 计.在得到该线性大系统的分散控制器后,可通过分散坐标变换的逆变换将线性大系统的控 制器变换为原非线性大系统的控制器.同时,控制器的分散性保持不变.该方法明显地降低了 该类非线性大系统分散控制器的设计难度.     

一般非线性系统的相关阶与线性化

讨论了一般非线性控制系统的线性化问题．基于一般非线性系统相关阶的概念,以微分几何方法为工具,给出一般非线性系统可线性化的一个充要条件,分析了相关阶、特征函数和系统维数的关系,并严格证明了线性化判据的必要性．     

A Global Maximum Error Controller Based Nonlinearity Aware TPWL Method for Reducing Nonlinear Systems

Abstract

Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.     

Achieving vector relative degree for nonlinear systems with parametric uncertainties

Several algorithms for adaptive control, as well as for static state feedback decoupling, feedback linearization, or inversion of nonlinear multivariable systems require that the systems have full vector relative degree, in order to be applied. In this paper, we provide a parameter-independent method of achieving full vector relative degree for nonlinear multivariable systems which do not have it. We determine conditions under which a diagonal dynamic precompensation is sufficient to achieve vector relative degree for multivariable nonlinear systems, and describe a simple algorithm which determines such compensation.     

An extended linearization approach to nonlinear system inversion

The inversion problem for nonlinear systems is considered from both the internal viewpoint (state-equation representations) and the external viewpoint (Volterra-series representations). In order to circumvent difficulties in the known, exact inversion theory, a method for obtaining what will be called a partial inverse system is proposed. For a given nonlinear system, a cascade system, typically containing differentiators, is found such that the overall nonlinear system has a family of constant operating points with inputs and outputs identical. Furthermore, the linearization of the overall system about each of these constant operating points is the identity system.     

一种基于等效线性化的非平稳随机动力响应分析的显式迭代算法

提出了一种基于等效线性化法的非平稳随机动力响应分析的显式迭代算法.首先根据等效线性化法把非线性系统转化为离散的线性系统,然后应用Newmark-β积分方法,推导出各个离散时刻的时域显式迭代公式,进而可以快速得到非线性系统的随机动力响应,最后用一个非线性的范德波尔系统和一个杜芬系统受非平稳随机荷载的算例验证了该算法的计算精度和计算效率.