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

Fractional Differential Equations

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

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

In this paper, a control structure that makes possible the integration of a kinematic controller and an adaptive fuzzy controller for trajectory tracking is developed for nonholonomic mobile robots. The system uncertainty, which includes mobile robot parameter variation and unknown nonlinearities, is estimated by a fuzzy logic system (FLS). The proposed adaptive controller structure represents an amalgamation of nonlinear processing elements and the theory of function approximation using FLS. The real-time control of mobile robots is achieved through the online tuning of FLS parameters. The system stability and the convergence of tracking errors are proved using the Lyapunov stability theory. Computer simulations are presented which confirm the effectiveness of the proposed tracking control law. The efficacy of the proposed control law is tested experimentally by a differentially driven mobile robot. Both simulation and results are described in detail.

Design and implementation of an adaptive fuzzy logic-based controller for wheeled mobile robots

This work proposes a novel combined model reference adaptive controller (MRAC) for unknown multi input multi output (MIMO) LTI systems with guaranteed parameter convergence. An online plant-parameter identification method is developed in conjunction with a direct control-parameter update law to ensure exponential convergence (after a tunable finite time) of tracking error as well as plant and control-parameter estimation errors to zero. Unlike the restrictive persistence of excitation (PE) condition required in classical MRAC approaches, this method guarantees parameter convergence by imposing a significantly milder initial excitation condition on the relevant signals. The introduction of a low-pass filter obviates the need for state derivative knowledge, whereas, the novel inclusion of an integral-like update in the plant-parameter estimation law overcomes the requirement of the restrictive PE condition. As far as the authors are aware, this is the first work on MRAC for MIMO linear time invariant (LTI) systems, which guarantees exponential convergence of the error dynamics without requiring the PE condition as well as the structural knowledge of the system matrices.

Combined MRAC for Unknown MIMO LTI Systems With Parameter Convergence

This paper proposes a computationally efficient artificial neural network (ANN) model for system identification of unknown dynamic nonlinear discrete time systems. A single layer functional link ANN is used for the model where the need of hidden layer is eliminated by expanding the input pattern by Chebyshev polynomials. Thus, creation of nonlinear decision boundaries in the multidimensional input space and approximation of complex nonlinear systems becomes easier. These models are linear in their parameters and nonlinear in the inputs. The recursive least squares method with forgetting factor is used as on-line learning algorithm for parameter updation. The good behaviour of the identification method is tested on Box and Jenkins Gas furnace benchmark identification problem, single input single output (SISO) and multi input multi output (MIMO) discrete time plants. Stability of the identification scheme is also addressed.

On-line system identification of complex systems using Chebyshev neural networks

Nonlinear System Identification using Neural Networks

This paper proposes a new adaptive-robust control (ARC) strategy for a tracking control problem of a class of uncertain Euler–Lagrange systems. The proposed adaptive-robust time-delay control (ARTDC) amalgamates the ARC strategy with the time-delay control (TDC). It comprises three parts: a time-delay estimation part, a desired dynamics injection part, and an adaptive-robust part. The main feature of the proposed ARTDC is that it does not involve any threshold value in its adaptive law; thus, it allows the switching gain to increase or decrease whenever the error trajectories move away or close to the switching surface, respectively. Thus, compared with the existing ARC schemes, ARTDC is able to alleviate the over- and underestimation problems of the switching gain. Moreover, the stability analysis of ARTDC provides an upper bound for the selection of sampling interval and its relation with controller gains. The proposed ARTDC shows improved tracking performance compared with the TDC and the existing adaptive sliding-mode control in simulations as well as in experiments with a multiple-degree-of-freedom system.

Indra Narayan Kar

Papers

Design and implementation of an adaptive fuzzy logic-based controller for wheeled mobile robots

Combined MRAC for Unknown MIMO LTI Systems With Parameter Convergence

On-line system identification of complex systems using Chebyshev neural networks

Nonlinear System Identification using Neural Networks

Adaptive-Robust Time-Delay Control for a Class of Uncertain Euler–Lagrange Systems