非线性系统的分层控制问题研究

发布时间：2018-05-18 05:18

本文选题：分层控制 + 原始系统　；参考：《中国科学技术大学》2017年博士论文

【摘要】：在过去的十多年间,线性和非线性系统的分层控制问题已有相当多的研究。简单来说,这个问题是为一个复杂系统设计一个控制律以使得其输出轨迹满足一些渐近性质和一些输出要求,例如区域可达性,区域不变性以及避障等。由于系统动态的复杂性和控制目标的多样性,通常直接进行系统控制以实现控制目标是非常困难的。而分层方法以一种间接的方式来解决这个问题。它通过构建一个简单系统得到一个层次结构。位于低层的是我们最终需要控制的原始系统,而高层系统包括了一个简单的抽象系统,用来简化控制器设计并减少复杂性。两层系统被所谓的接口连接起来。接口可以驱动原始系统的输出近似跟踪到高层抽象系统的输出。当抽象系统达到控制目标时,原始系统也可以达到相应的目标。另外,一个称为模拟函数的概念可以用来帮助我们设计系统接口。分层控制理论已经应用于一些研究领域,包括机器人学、机械电子学、多智能体系统等。本论文主要研究非线性原始系统和线性抽象系统之间的接口设计。主要研究内容包括以下几个方面。首先,我们赋予了接口概念新的含义。在之前的工作中,接口为接口函数的简称,它假设原始系统的所有状态信息是可得的。具有输出反馈形式或者包含有一个微分方程的分层控制器从未被考虑过。为了将这种情况纳入考虑范围,我们引入了接口动态的概念。接口不仅仅意味着接口函数,同时也是指接口动态。在这个设定下,我们可以在一个框架下设计状态反馈控制器和输出反馈控制器。另外,我们重新表述了分层控制问题。原来的表述只考虑了输出误差的瞬态响应,现在我们将一些稳态约束也加入这个问题,使得它在一定程度上包含了渐近跟踪问题。其次,我们为线性系统设计了两类接口:接口函数和接口动态。对于线性系统,我们构造了一个抽象系统使得我们能基于抽象系统的反馈增益来得到一个新的接口函数,并且能以一个低阶的正定矩阵表征新的模拟函数。换句话说,解决分层控制问题时我们需要的仅仅是抽象系统的信息而不是原始系统的信息,很明显,前者比后者更容易得到。至于输出反馈分层控制问题,我们使用状态观测器设计了一个接口动态。然后,对于一般的非线性系统,我们用反馈线性化方法设计了一个接口函数。由于在实际情况下,系统内动态部分状态经常是不可得的,所以我们设计了一个只使用系统输出及其各阶导数的接口函数。同时,对于一类非线性系统,我们通过高增益观测器实现了一个只利用输出信息的接口动态,其中观测器用来产生系统输出的导数的估计值。随后,我们用一个单链机械臂系统的例子说明了所提出方法的有效性。至于含有不确定性参数的对象模型,其分层控制问题尚无研究。本文借助于输出调节领域的内模概念,通过递归过程得到了一个鲁棒型的输出接口动态,其中内模的作用是渐近重构控制器中的前馈项。然后我们又设计了一个自适应型的接口动态。最后,我们讨论了大型网络控制系统的分层问题。作为一个传统模拟函数的自然扩展,我们引入向量模拟函数的概念来研究互联系统之间的层次关系。通过构造一个比较系统,我们给出了关于这个问题的一个一般结论。当我们考虑一类互联非线性系统时,一个易检验的充分条件可以用来判断分层关系。最后基于这个条件,我们对线性互联系统提出了一个抽象系统构造方法。
[Abstract]:In the past more than 10 years, there have been considerable research on the hierarchical control problem of linear and nonlinear systems. Simply, the problem is to design a control law for a complex system to make its output trajectory satisfied with some asymptotic properties and some output requirements, such as regional accessibility, regional invariance, and obstacle avoidance. The complexity of the dynamic system and the diversity of controlling the target is often difficult to carry out direct system control to achieve the control goal. The hierarchical approach solves this problem in an indirect way. It gets a hierarchical structure by building a simple system. The low level is the original system that we eventually need to control. The high level system includes a simple abstract system to simplify the design of the controller and reduce the complexity. The two layer system is connected by the so-called interface. The interface can drive the output of the original system approximately to the output of the high level abstract system. When the abstract system reaches the control target, the original system can also achieve the corresponding target. In addition, a concept called analog function can be used to help us to design the system interface. The hierarchical control theory has been applied to some research fields, including robotics, mechanical electronics, multi-agent systems and so on. This paper mainly studies the interface design between the nonlinear original system and the linear pumping system. First, we have given the new meaning of the interface concept. In the previous work, the interface is the abbreviation of the interface function, which assumes that all the state information of the original system is available. A hierarchical controller with output feedback or a differential equation has never been considered. Considering the scope, we introduce the concept of interface dynamics. Interfaces not only mean interface functions, but also interface dynamics. Under this setting, we can design a state feedback controller and an output feedback controller under a framework. In addition, we reexpress the layer control problem. The original statement only takes into account the output error. The poor transient response, we now add some steady state constraints to this problem, so that it contains the asymptotic tracking problem to some extent. Secondly, we have designed two kinds of interfaces for linear systems: interface functions and interface dynamics. For linear systems, we construct an abstract system that allows us to be based on the inverse of the abstract system. In other words, we need only the information of the abstract system but not the information of the original system when solving the problem of stratified control. It is obvious that the former is easier to get than the latter. As for the output feedback stratified control question, it is obvious that the former is more easy to get. We use the state observer to design an interface dynamics. Then, for the general nonlinear system, we use the feedback linearization method to design an interface function. In the actual case, the dynamic partial state in the system is often inaccessible, so we set up a single use of the system output and its derivatives. At the same time, for a class of nonlinear systems, we implement an interface dynamics that only uses the output information through a high gain observer, in which the observer is used to generate the estimation of the derivative of the output of the system. Then, we use an example of a single chain manipulator system to illustrate the effectiveness of the proposed method. The problem of hierarchical control for qualitative parameters is not yet studied. In this paper, a robust output interface dynamic is obtained by recursive procedure with the help of the internal model concept in the field of output regulation. The function of the internal model is to reconstruct the feedforward item in the controller. Then we also design an adaptive interface dynamic. Then we discuss the stratification of large network control systems. As a natural extension of a traditional analogue function, we introduce the concept of vector analog functions to study the hierarchical relationship between interconnected systems. By constructing a comparative system, we give a general conclusion on this question. In conjunction with a nonlinear system, a easily verifiable sufficient condition can be used to judge the stratified relationship. Finally, based on this condition, we propose an abstract system construction method for linear interconnected systems.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP13

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