There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Presents a design methodology for stabilization of a class of nonlinear systems. First, the authors represent a nonlinear plant with a Takagi-Sugeno fuzzy model. Then a model-based fuzzy controller design utilizing the concept of the so-called "parallel distributed compensation" is employed. The main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system. The design procedure is conceptually simple and natural. Moreover, the stability analysis and control design problems can be reduced to linear matrix inequality (LMI) problems. Therefore, they can be solved efficiently in practice by convex programming techniques for LMIs. The design methodology is illustrated by application to the problem of balancing and swing-up of an inverted pendulum on a cart.

An approach to fuzzy control of nonlinear systems: stability and design issues

Fuzzy controllers are a class of knowledge based controllers using artificial intelligence techniques with origins in fuzzy logic. They can be found either as stand-alone control elements or as int ...

An Introduction to Fuzzy Control

Fundamental and advanced developments in neuro-fuzzy synergisms for modeling and control are reviewed. The essential part of neuro-fuzzy synergisms comes from a common framework called adaptive networks, which unifies both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called adaptive-network-based fuzzy inference system (ANFIS), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neuro-fuzzy approaches are also addressed. >

https://ir.nctu.edu.tw:443/bitstream/11536/2013/1/A1995QJ99800003.pdf

Neuro-fuzzy modeling and control

This paper presents a method to address the problem of presence of a bias component in the input sinusoidal signal of the EKF frequency tracker. The bias component may be intrinsically present in the input signal or may be generated due to temporary system faults or can be generated by measurement devices. A new state space model has been developed for parameter estimation of a biased sinusoidal signal in Gaussian noise using extended Kalman filter (EKF). The proposed model not only has the ability of estimating constant parameters, but also tracks variations in the bias component and frequency. Simulation results demonstrate the desirable performance of the proposed EKF for parameter estimation of a biased sinusoidal signal.

An extended Kalman filter for identification of biased sinusoidal signals

In this paper the Newton-based extremum seeking for an unknown static map which is coupled with a diffusion partial differential equation (PDE) is presented. In contrast with previous works where optimization takes place at the zero boundary of the diffusion PDE, this paper considers a more general case where the optimization can take place at an arbitrary interior point of the diffusion PDE. First, the additive and multiplicative dither signals are designed to provide the estimations of the gradient and Hessian of the map in the average sense. Then, the error system is formulated as a first-order ordinary differential equation (ODE) coupled with a diffusion PDE at an interior point and an explicit dynamic feedback law is designed for stabilizing it. By using the backstepping transformation and infinite dimensional averaging theorem, it is shown that the proposed scheme achieves local exponential convergence to a neighborhood of the extremum. A simulation example is given to illustrate the theoretical results.

Newton-based extremum seeking for a static map coupled with a diffusion PDE at an arbitrary interior point

In this paper, a consensus problem is addressed for first-order multi-agent systems with unknown nonlinear dynamics under undirected graphs. Adaptive fuzzy wavelet networks are used to design two n...

Consensus in first-order nonlinear multi-agent systems with state time delays using adaptive fuzzy wavelet networks:

Consensus in networks of uncertain euler-lagrange agents using adaptive gravity compensation

A Fast Fuzzy-Based (omega, alpha)-Fair Rate Allocation Algorithm.

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