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Robust Stability for Nonlinear Control: Analysis and Synthesis

非线性控制的鲁棒稳定性：分析与综合

基本信息

批准号：
EP/F035950/1
负责人：
Mark French
金额：
$ 36.59万
依托单位：
University of Southampton
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2008
资助国家：
英国
起止时间：
2008 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FF035950%2F1
关键词：
Robust Stability Nonlinear Control Analysis

项目摘要

Robustness is the key concept for modern control theory: it concerns the ability of a control system to work not only for the mathematical model of the system to be controlled, but also to work in the `real world' where the true system always deviates from the model. For linear systems, control engineers have developed significant approaches to addresses this issue (for example H-infinity control).In the past decade substantial progress in the development of a robust control theory for nonlinear systems has also been made, but this subject is very much in its infancy. Here we consider the input-output theory based on the 1997 development of the `nonlinear gap metric' due to Georgiou and Smith. A notable limitation this existing nonlinear input output theory is that it only directly applies to systems which start at rest. The core part of this proposal is to undertake the substantial generalisation of this theory to the case of systems which do not start at equilibrium positions. This approach may in part involve a unification of the nonlinear 'state-space' due to Sontag (which handles non-zero initial conditions, but robustness is not an explicit part of the framework) with the input-output theory (in which robustness is the central issue, but non zero initial conditions are not handled).Two substantial applications of the underlying theory will then be investigated.1. Nonlinear seperation principles. Such principles describe conditions under which a controller based on information about the state can be replaced by a controller based only on the feedback of the measured output. Here we are seeking to use the input-output tools to substantially extend the existing results in the literature; to explicitly handle robustness to unmodelled dynamics and disturbances at both the input and the output of the system.2. Nonlinear complexity reduction. A substantial obstacle to many of the control designs developed in nonlinear control theory, is that for systems of moderate order, the recursive nature of the design constructions means that the explicit formulae for the controller have a very rapid growth (with the order of the system) in the number of terms. This means the expressions are too large and unwieldy for practical purposes for systems of moderate order. Complexity reduction aims to reduce the complexity of these expressions in a systematic way, whilst keeping control of the consequent altered robustness and performance of the control system.Problems 1. and 2. are important in their own right, and we will be introducing a completely new armoury of tools into the relevant literature. Importantly also, these applications will serve to illustrate the power of the core input-output approach.

鲁棒性是现代控制理论的关键概念：它涉及控制系统不仅对被控系统的数学模型起作用，而且在真实系统总是偏离模型的“真实的世界”中起作用的能力。对于线性系统，控制工程师已经开发了解决这个问题的重要方法（例如H无穷控制）。在过去的十年中，非线性系统的鲁棒控制理论的发展也取得了实质性进展，但该学科还处于起步阶段。在这里，我们考虑的投入产出理论的基础上，1997年的发展的“非线性间隙度量”由于Georgiou和史密斯。现有的非线性输入输出理论的一个显著的局限性是它只能直接应用于静止起动的系统。这一建议的核心部分是承担这一理论的大量推广的情况下，系统不开始在平衡的位置。这种方法可能部分地涉及到由于Sontag的非线性“状态空间”（它处理非零初始条件，但鲁棒性不是框架的明确部分）与输入输出理论（鲁棒性是核心问题，但不处理非零初始条件）的统一。非线性分离原理这样的原理描述了这样的条件，在该条件下，基于关于状态的信息的控制器可以被仅基于测量输出的反馈的控制器替换。在这里，我们正在寻求使用的输入输出工具，大大扩展了现有的文献中的结果，明确地处理鲁棒性未建模的动态和干扰的输入和输出的系统。非线性复杂度降低。在非线性控制理论中开发的许多控制设计的一个实质性障碍是，对于中等阶的系统，设计构造的递归性质意味着控制器的显式公式在项的数量上具有非常快速的增长（随着系统的阶数）。这意味着表达式对于中等阶系统的实际目的来说太大和笨拙。复杂性降低的目的是以系统的方式降低这些表达式的复杂性，同时保持对控制系统的随之改变的鲁棒性和性能的控制。和2.它们本身就很重要，我们将在相关文献中引入一系列全新的工具。同样重要的是，这些应用将有助于说明核心投入产出方法的力量。