第3章 Fuzzy Identification and Estimation
1 第3章 Fuzzy Identification and Estimation
教学内容 这一章主要研究了怎样用模糊进行评估和辨识。 模糊辨识设计的最主要的问题是怎样用己知的离 散数据构建一个模糊系统。首先介绍最基本的函 数近似问题,然后介绍了传统的辨识方法:最小 二乘法即怎样用批量最小二乘法和递归最小二乘 法来辨识一个系统以匹酲输入输出数据。最后讲 述用这两种方法直接训练模糊系统。 本章将现代控制理论的自适应控制理论应用于模 糊控制技术中,以期提高模糊控制系统的动态、 静态性能,增强模糊控制系统对于模型的参数、 结构变化的鲁棒性以及控制系统不同相应阶段对 控制其性能的不同要求,提高控制系统的综合品 质
2 教学内容： ◼ 这一章主要研究了怎样用模糊进行评估和辨识。 模糊辨识设计的最主要的问题是怎样用已知的离 散数据构建一个模糊系统。首先介绍最基本的函 数近似问题，然后介绍了传统的辨识方法：最小 二乘法即怎样用批量最小二乘法和递归最小二乘 法来辨识一个系统以匹配输入输出数据。最后讲 述用这两种方法直接训练模糊系统。 ◼ 本章将现代控制理论的自适应控制理论应用于模 糊控制技术中，以期提高模糊控制系统的动态、 静态性能，增强模糊控制系统对于模型的参数、 结构变化的鲁棒性以及控制系统不同相应阶段对 控制其性能的不同要求，提高控制系统的综合品 质
主要内容 直接自适应控制和间接自适应控制 的基本概念; 2.模糊模型参考学习控制( FMRLO) 的原理、结构; 3. FMRLO的设计和实现
3 主要内容： 1. 直接自适应控制和间接自适应控制 的基本概念； 2. 模糊模型参考学习控制（ FMRLC ） 的原理、结构； 3. FMRLC 的设计和实现
教学重点: 详细阐述了用一个函数拟和输入输出数 据所应注意的问题,同时还阐述了怎样 将语言变量信息转化为函数,以便用该 函数来拟和输入输出数据。其中输入输 出数据的选择关系着辨识结果的好坏, 通常要求其能对系统充分激励 模糊模型参考学习控制( FMRLC)的 原理和结构
4 教学重点： ◼ 详细阐述了用一个函数拟和输入输出数 据所应注意的问题，同时还阐述了怎样 将语言变量信息转化为函数，以便用该 函数来拟和输入输出数据。其中输入输 出数据的选择关系着辨识结果的好坏， 通常要求其能对系统充分激励。 ◼ 模糊模型参考学习控制（FMRLC）的 原理和结构
教学难点 ■对 FMRLO中学习机制的准确把握和理解, 关键是模糊逆模型的设计
5 教学难点： ◼ 对FMRLC中学习机制的准确把握和理解, 关键是模糊逆模型的设计
教学要求: ■本章的学习需要预先掌握一定的自适应控 制、自校正调节器的基础知识、概念。要 求掌握模糊模型参考学习控制( FMRLC) 的原理和结构。 当离散数据是通过试验获得的输入输出数 据的时候,我们就可以通过数据来辨识 个模糊系统的模型;当数据是通过其它的 途径获得时,可以对数据进行插补处理 然后用处理过的数据来辨识模糊系统
6 教学要求： ◼ 本章的学习需要预先掌握一定的自适应控 制、自校正调节器的基础知识、概念。要 求掌握模糊模型参考学习控制（FMRLC） 的原理和结构。 ◼ 当离散数据是通过试验获得的输入输出数 据的时候，我们就可以通过数据来辨识一 个模糊系统的模型；当数据是通过其它的 途径获得时，可以对数据进行插补处理， 然后用处理过的数据来辨识模糊系统
3.1 Overview While up to this point we have focused on control, in this chapter we will examine how to use fuzzy systems for estimation and identification The numerical data. This is in contrast to our discussion in Chapters 2 and/ basic problem to be studied here is how to construct a fuzzy system fror where we used linguistics as the starting point to specify a fuzzy system. If the numerical data is plant input-output data obtained from an experiment we may identify a fuzzy system model of the plant. This may be useful for simulation purposes and sometimes for use in a controller On the other hand, the data may come from other sources, and a fuzzy system may be used to provide for a parameterized nonlinear function that fits the data by using its asic interpolation capabilities. For instance, suppose that we have a human expert who controls some process and we observe how she or he does this by observing what numerical plant input the expert picks for the given numerical data that she or he observes. Suppose further that we have many such associations between "decision-making data. "The methods in this chapter will show how to constructrules for a fuzzy controller from this data (i.e, identify a controller from the human-generated decision-making data) and in this sense they provide another method to design controllers 7
7 3.1 Overview ◼ While up to this point we have focused on control, in this chapter we will examine how to use fuzzy systems for estimation and identification. The basic problem to be studied here is how to construct a fuzzy system from numerical data. This is in contrast to our discussion in Chapters 2 and 3, where we used linguistics as the starting point to specify a fuzzy system. If the numerical data is plant input-output data obtained from an experiment, we may identify a fuzzy system model of the plant. This may be useful for simulation purposes and sometimes for use in a controller. On the other hand, the data may come from other sources, and a fuzzy system may be used to provide for a parameterized nonlinear function that fits the data by using its basic interpolation capabilities. For instance, suppose that we have a human expert who controls some process and we observe how she or he does this by observing what numerical plant input the expert picks for the given numerical data that she or he observes. Suppose further that we have many such associations between "decision-making data." The methods in this chapter will show how to construct rules for a fuzzy controller from this data (i.e., identify a controller from the human-generated decision-making data), and in this sense they provide another method to design controllers
Yet another problem that can be solved with the methods in this chapter is that of how to construct a fuzzy system that will serve as a parameter estimator. To do this, we need data that shows, roughly how the input-output mapping of the estimator should behave (i.e, how it should estimate). One way to generate this data is to begin by establishing a simulation test bed for the plant for which parameter estimation must be performed. Then a set of simulations can be conducted, each with a different value for the parameter to be estimated. by coupling the test conditions and simulation-generated data with the parameter values, you can gather appropriate data pairs that allow for the construction of a fuzzy estimator, For some plants it may be possible to perform this procedure with actual experimental data(by physically adjusting the parameter to be estimated). In a similar way, you could construct fuzzy predictors using the approaches developed in this chapter
8 ◼ Yet another problem that can be solved with the methods in this chapter is that of how to construct a fuzzy system that will serve as a parameter estimator. To do this, we need data that shows, roughly how the input-output mapping of the estimator should behave (i.e., how it should estimate). One way to generate this data is to begin by establishing a simulation test bed for the plant for which parameter estimation must be performed. Then a set of simulations can be conducted, each with a different value for the parameter to be estimated .by coupling the test conditions and simulation-generated data with the parameter values, you can gather appropriate data pairs that allow for the construction of a fuzzy estimator, For some plants it may be possible to perform this procedure with actual experimental data (by physically adjusting the parameter to be estimated). In a similar way, you could construct' fuzzy predictors using the approaches developed in this chapter
We begin this chapter by setting up the basic function approxi on problem in See where we provide an overview of some of the fundamental issues in how to fit a function to input output data, including how to incorporate linguistic information into the function that we are trying to force to match the data. We explain how to measure how well a function fits data and provide an example of how to choose a data set for an engine failure estimation problem(a type of parameter estimation problem in which when estimates of the parameters take on certain values, we say that a failure has occurred)
9 ◼ We begin this chapter by setting up the basic function approximation problem in Section 3.2, where we provide an overview of some of the fundamental issues in how to fit a' function to inputoutput data, including how to incorporate linguistic information into the function that we are trying to force to match the data. We explain how to measure how well a function fits data and provide an example of how to choose a data set for an engine failure estimation problem (a type of parameter estimation problem in which when estimates of the parameters take on certain values, we say that a failure has occurred)
a In section 3. 3 we introduce conventional lo d least sql cares methods for identification, explain how they can be used to tune fuzzy systems, provide a simple example, and offer examples of how they can be used to train fuzzy systems-Next in Section 3, 4 we show how gradient methods can be used to train a standard and Takagi-Sugeno fuzzy system, These methods are quite similar to the ones used to train neural networks(e.g, the" back-propagation technique). We provide examples for standard and Takagi-Sugeno fuzzy systems. We highlight the fact that via either the recursive least squares method for fuzzy systems or the gradient method we can perform on-line parameter estimation. We will see in Chapter 6 that these methods can be combined with a controller construction procedure to provide a method for adaptive fuzzy control 10
10 ◼ In Section 3,3 we introduce conventional least squares methods for identification, explain how they can be used to tune fuzzy systems, provide a simple example, and offer examples of how they can be used to train fuzzy systems- Next, in Section 3,4 we show how gradient methods can be used to train a standard and Takagi-Sugeno fuzzy system, These methods are quite similar to the ones used to train neural networks (e.g., the "back-propagation technique"). We provide examples for standard and Takagi-Sugeno fuzzy systems. We highlight the fact that via either the recursive least squares method for fuzzy systems or the gradient method we can perform on-line parameter estimation. We will see in Chapter 6 that these methods can be combined with a controller construction procedure to provide a method for adaptive fuzzy control