This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

Probability and Measure

Binary grey wolf optimization approaches for feature selection

In classification, feature selection is an important data pre-processing technique, but it is a difficult problem due mainly to the large search space. Particle swarm optimisation (PSO) is an efficient evolutionary computation technique. However, the traditional personal best and global best updating mechanism in PSO limits its performance for feature selection and the potential of PSO for feature selection has not been fully investigated. This paper proposes three new initialisation strategies and three new personal best and global best updating mechanisms in PSO to develop novel feature selection approaches with the goals of maximising the classification performance, minimising the number of features and reducing the computational time. The proposed initialisation strategies and updating mechanisms are compared with the traditional initialisation and the traditional updating mechanism. Meanwhile, the most promising initialisation strategy and updating mechanism are combined to form a new approach (PSO(4-2)) to address feature selection problems and it is compared with two traditional feature selection methods and two PSO based methods. Experiments on twenty benchmark datasets show that PSO with the new initialisation strategies and/or the new updating mechanisms can automatically evolve a feature subset with a smaller number of features and higher classification performance than using all features. PSO(4-2) outperforms the two traditional methods and two PSO based algorithm in terms of the computational time, the number of features and the classification performance. The superior performance of this algorithm is due mainly to both the proposed initialisation strategy, which aims to take the advantages of both the forward selection and backward selection to decrease the number of features and the computational time, and the new updating mechanism, which can overcome the limitations of traditional updating mechanisms by taking the number of features into account, which reduces the number of features and the computational time.

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Particle swarm optimisation for feature selection in classification

A survey on new generation metaheuristic algorithms

In this paper, some statistical quantities of the distortion caused by noise in the rule base of type-2 fuzzy logic systems are calculated. In many papers, the justification of better performance of type-2 fuzzy logic systems over type-1 counterparts in noisy conditions are studied only for some specific cases. In this paper, a simple type-2 fuzzy logic system with the ellipsoidal membership function is considered. Using this fuzzy system, it is possible to statistically study the effect of noise in the rule base of fuzzy systems. Using this statistical analysis, it is shown that the type-2 fuzzy logic systems with ellipsoidal membership function is less influenced in the presence of high level of noise when compared to its type-1 counterparts.

Statistical results to show the superiority of type two fuzzy logic systems over type one counterparts under noisy conditions

The major challenge in the design of Interval type-2 fuzzy logic system (IT2FLS) is to determine the optimal parameters for their antecedent and consequent parts. This paper propose a novel hybrid learning algorithm for the design of IT2FLS. The proposed hybrid learning algorithm utilizes the combination of extreme learning machine (ELM) and artificial bee colony optimization (ABC) to tune the parameters of the consequent and antecedent parts of the IT2FLS, respectively. The effective forecasting performance of the proposed hybrid learning algorithm is analyzed by modeling a chaotic data set. It is found that the forecasted errors gradually decrease with decrease in the level of noise in data and vise versa.

Artificial bee colony optimization of interval type-2 fuzzy extreme learning system for chaotic data

This paper presents a novel approach to identify the prediction interval associated with data using interval type-2 fuzzy logic systems with support vector regression. For such a purpose, a constrained quadratic objective function is defined which is then solved using well-established quadratic programming approaches. Not only does the output of interval type-2 fuzzy logic system replicates the measured value, but also it provides the lower bound and the upper bound for measured data values. In the proposed approach, to have more valuable information, a penalty term is added in the cost functions to have full control over the width of prediction interval. This method has been successfully applied to two benchmark identification problems. It is observed that by using the control parameter in the cost function, it is possible to obtain a narrower, yet inclusive prediction interval. Furthermore, superior prediction accuracy is obtained compared to existing methods in literature. Motivated by these results, the proposed approach is used to predict time series collected using a satellite from Urmia lake water level which resulted in high accuracy and an inclusive prediction interval. The graphical abstract presented for the paper illustrates the overall data gathering as well as data analysis made to estimate the prediction interval associated with Urmia lake water level data.

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Prediction Interval Identification Using Interval Type-2 Fuzzy Logic Systems: Lake Water Level Prediction Using Remote Sensing Data

In this paper a novel type reducer for interval type-2 fuzzy systems is proposed. Type reduction of interval type-2 fuzzy systems requires the solution of two nonlinear constrained optimization problems. Existing exact solutions to these problems (Karnik-Mendel algorithms and their variants) require sorting which is known to be computationally very expensive. In this research, these optimization problems are reformulated and novel improved solutions to these problem are proposed which do not require sorting any more. Simulation results show that the results obtained using the proposed methods are exactly the same as that of enhanced Karnik-Mendel algorithms with at least 9% less computational time when the number of rules of fuzzy system is bigger than ten. For more number of rules, it is even possible that the proposed methods converge 37% faster than enhanced Karnik-Mendel algorithms. In addition, it is shown that the computational time required by the proposed methods grow linearly as the number of the rules increases.

Improved Karnik-Mendel algorithm: Eliminating the need for sorting

Non-iterative methods for parameter estimation for interval type-2 neuro-fuzzy structure are fast to implement, when compared to online methods, and need no –or a few– parameters to be tuned. In this paper, a novel dynamic cost function, which defines a relationship between the current and past errors, is defined. The minimization of the aforementioned cost function results in a decreasing sequence of error which makes the proposed method numerically more stable when compared to least squares-based methods. It is a well-known phenomenon that a matrix inversion may cause problems if the matrix to be inverted is ill-defined i.e. its condition number is far bigger than one. The use of a dynamic relationship between the current and past error adds more degrees of freedom which makes it possible to improve the condition number of the matrix. Comprehensive simulation studies are presented for the prediction of financial data sets. The simulation results shows the superior numerical stability of the proposed method as the mean value of the condition number is smaller. This finding results in more accurate matrix inversion to be done in the two-step matrix inversion.

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Mojtaba Ahmadieh Khanesar

Papers

Statistical results to show the superiority of type two fuzzy logic systems over type one counterparts under noisy conditions

Artificial bee colony optimization of interval type-2 fuzzy extreme learning system for chaotic data

Prediction Interval Identification Using Interval Type-2 Fuzzy Logic Systems: Lake Water Level Prediction Using Remote Sensing Data

Improved Karnik-Mendel algorithm: Eliminating the need for sorting

A Novel Non-Iterative Parameter Estimation Method for Interval Type-2 Fuzzy Neural Networks Based on a Dynamic Cost Function