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

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

A tutorial account of variable structure control with sliding mode is presented. The purpose is to introduce in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach. This approach is particularly attractive for the control of nonlinear systems. Prominent characteristics such as invariance, robustness, order reduction, and control chattering are discussed in detail. Methods for coping with chattering are presented. Both linear and nonlinear systems are considered. Future research areas are suggested and an extensive list of references is included. >

Variable structure control: a survey

We present the theory and design of interval type-2 fuzzy logic systems (FLSs). We propose an efficient and simplified method to compute the input and antecedent operations for interval type-2 FLSs: one that is based on a general inference formula for them. We introduce the concept of upper and lower membership functions (MFs) and illustrate our efficient inference method for the case of Gaussian primary MFs. We also propose a method for designing an interval type-2 FLS in which we tune its parameters. Finally, we design type-2 FLSs to perform time-series forecasting when a nonstationary time-series is corrupted by additive noise where SNR is uncertain and demonstrate an improved performance over type-1 FLSs.

https://sipi.usc.edu/~mendel/publications/Liang%26Mendel%20TFS%2010-00%20%232.pdf

Interval type-2 fuzzy logic systems: theory and design

Networked control systems (NCSs) have, in recent years, brought many innovative impacts to control systems. However, great challenges are also met due to the network-induced imperfections. Such network-induced imperfections are handled as various constraints, which should appropriately be considered in the analysis and design of NCSs. In this paper, the main methodologies suggested in the literature to cope with typical network-induced constraints, namely time delays, packet losses and disorder, time-varying transmission intervals, competition of multiple nodes accessing networks, and data quantization are surveyed; the constraints suggested in the literature on the first two types of constraints are updated in different categorizing ways; and those on the latter three types of constraints are extended.

Network-Induced Constraints in Networked Control Systems—A Survey

This paper provides an overview of the recent developments in data-based techniques focused on modern industrial applications. As one of the hottest research topics for complicated processes, the data-based techniques have been rapidly developed over the past two decades and widely used in numerous industrial sectors nowadays. The core of data-based techniques is to take full advantage of the huge amounts of available process data, aiming to acquire the useful information within. Compared with the well-developed model-based approaches, data-based techniques provide efficient alternative solutions for different industrial issues under various operating conditions. The main objective of this paper is to review and summarize the recent achievements in data-based techniques, especially for complicated industrial applications, thus providing a referee for further study on the related topics both from academic and practical points of view. This paper begins with a brief evolutionary overview of data-based techniques in the last two decades. Then, the methodologies only based on process measurements and the model-data integrated techniques will be further introduced. The recent developments for modern industrial applications are, respectively, presented mainly from perspectives of monitoring and control. The new trends of data-based technique as well as potential application fields are finally discussed.

Data-Based Techniques Focused on Modern Industry: An Overview

The stability of discrete-time sliding mode control systems is investigated and a new sliding mode condition is suggested. It is shown that the control must have upper and lower bounds. A numerical example is discussed as an illustration.

On the stability of discrete-time sliding mode control systems

Being able to forecast time series accurately has been quite a popular subject for researchers both in the past and at present. However, the lack of ability of conventional analysis methods to forecast time series that are not smooth leads the scientists and researchers to resort to various forecasting models that have different mathematical backgrounds, such as artificial neural networks, fuzzy predictors, evolutionary and genetic algorithms. In this paper, the accuracies of different grey models such as GM(1,1), Grey Verhulst model, modified grey models using Fourier Series is investigated. Highly noisy data, the United States dollar to Euro parity between the dates 01.01.2005 and 30.12.2007, are used to compare the performances of the different models. The simulation results show that modified grey models have higher performances not only on model fitting but also on forecasting. Among these grey models, the modified GM(1,1) using Fourier series in time is the best in model fitting and forecasting.

Grey system theory-based models in time series prediction

Sliding-mode control (SMC) has been studied extensively for over 50 years and widely used in practical applications due to its simplicity and robustness against parameter variations and disturbances. Despite the extensive research activities carried out, the key technical problems associated with SMC remain as challenging research questions due to demands for new industrial applications and technological advances. In this respect, soft computing (SC) is a rather recent development in intelligent systems which has provided alternative means for adaptive learning and control to overcome the key SMC technical problems. Substantial efforts in integration of SMC with SC have been placed in recent years with various successes. In this paper, we provide the state of the art of recent developments in SMC systems with SC, examining key technical research issues and future perspectives.

Okyay Kaynak

Papers

Network-Induced Constraints in Networked Control Systems—A Survey

Data-Based Techniques Focused on Modern Industry: An Overview

On the stability of discrete-time sliding mode control systems

Grey system theory-based models in time series prediction

Sliding-Mode Control With Soft Computing: A Survey