On robust estimation of the location parameter

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

The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

Data-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art.

Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control

In the structure of ANFIS, there are two different parameter groups: premise and consequence. Training ANFIS means determination of these parameters using an optimization algorithm. In the first ANFIS model developed by Jang, a hybrid learning approach was proposed for training. In this approach, while premise parameters are determined by using gradient descent (GD), consequence parameters are found out with least squares estimation (LSE) method. Since ANFIS has been developed, it is used in modelling and identification of numerous systems and successful results have been achieved. The selection of optimization method utilized in training is very important to get effective results with ANFIS. It is seen that derivate based (GD, LSE etc.) and non-derivative based (heuristic algorithms such us GA, PSO, ABC etc.) algorithms are used in ANFIS training. Nevertheless, it has been observed that there is a trend toward heuristic based ANFIS training algorithms for better performance recently. At the same time, it seems to be proposed in derivative and heuristic based hybrid algorithms. Within the scope of this study, the heuristic and hybrid approaches utilized in ANFIS training are examined in order to guide researchers in their study. In addition, the final status in ANFIS training is evaluated and it is aimed to shed light on further studies related to ANFIS training.

Adaptive network based fuzzy inference system (ANFIS) training approaches: a comprehensive survey

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

Model Predictive Control in Aerospace Systems: Current State and Opportunities

In this paper, a grey sliding-mode controller is proposed to regulate the wheel slip, depending on the vehicle forward velocity. The proposed controller anticipates the upcoming values of wheel slip and takes the necessary action to keep the wheel slip at the desired value. The performance of the control algorithm as applied to a quarter vehicle is evaluated through simulations and experimental studies that include sudden changes in road conditions. It is observed that the proposed controller is capable of achieving faster convergence and better noise response than the conventional approaches. It is concluded that the use of grey system theory, which has certain prediction capabilities, can be a viable alternative approach when the conventional control methods cannot meet the desired performance specifications.

A Grey System Modeling Approach for Sliding-Mode Control of Antilock Braking System

Emerging applications of quadrotor vertical take-off and landing (VTOL) unmanned aerial vehicles in various fields have created a need for demanding controllers that are able to counter several challenges, inter alia, nonlinearity, underactuated dynamics, lack of modeling, and uncertainties in the working environment. This study compares and contrasts type-1 and type-2 fuzzy neural networks (T2FNNs) for the trajectory tracking problem of quadrotor VTOL aircraft in terms of their tracking accuracy and control efforts. A realistic trajectory consisting of both straight lines and curvatures for a surveillance operation with minimum snap property, which is feasible regarding input constraints of the quadrotor, is generated to evaluate the proposed controllers. In order to imitate the outdoor noisy and time-varying working conditions, realistic uncertainties, such as wind and gust disturbances, are fed to the real-time experiment in the laboratory environment. Furthermore, a cost function based on the integral of the square of the sliding surface, which gives the optimal parameter update rules, is used to train the consequent part parameters of the T2FNN. Thanks to the learning capability of the proposed controllers, experimental results show the efficiency and efficacy of the learning algorithms that the proposed T2FNN-based controller with the optimal tuning algorithm is 50% superior to a conventional proportional-derivative (PD) controller in terms of control accuracy but requires more control effort. T2FNN structures are also shown to possess better noise reduction property as compared to their type-1 counterparts in the presence of unmodeled noise and disturbances.

Type-2 Fuzzy Logic Trajectory Tracking Control of Quadrotor VTOL Aircraft With Elliptic Membership Functions

In this paper, the use of extended Kalman filter for the optimization of the parameters of type-2 fuzzy logic systems is proposed. The type-2 fuzzy logic system considered in this study benefits from a novel type-2 fuzzy membership function which has certain values on both ends of the support and the kernel, and uncertain values on other parts of the support. To have a comparison of the extended Kalman filter with other existing methods in the literature, particle swarm optimization and gradient descent-based methods are used. The proposed type-2 fuzzy neuro structure is tested on different noisy input-output data sets, and it is shown that extended Kalman filter has a better performance as compared to the gradient descent-based methods. Although the performance of the proposed method is comparable with the particle swarm optimization method, it is faster and more efficient than the particle swarm optimization method. Moreover, the simulation results show that the proposed novel type-2 fuzzy membership function with the extended Kalman filter has noise rejection property. Kalman filter is also used to train the parameters of type-2 fuzzy logic system in a feedback error learning scheme. Then, it is used to control a real-time laboratory setup ABS and satisfactory results are obtained.

Erdal Kayacan

Papers

Grey system theory-based models in time series prediction

Model Predictive Control in Aerospace Systems: Current State and Opportunities

A Grey System Modeling Approach for Sliding-Mode Control of Antilock Braking System

Type-2 Fuzzy Logic Trajectory Tracking Control of Quadrotor VTOL Aircraft With Elliptic Membership Functions

Extended Kalman Filter Based Learning Algorithm for Type-2 Fuzzy Logic Systems and Its Experimental Evaluation