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"This monograph presents a unified mathematical framework for a wide range of problems in estimation and control. The authors discuss the two most commonly used methodologies: the stochastic H2 approach and the deterministic (worst-case) H� approach. Despite the fundamental differences in the philosophies of these two approaches, the authors have discovered that, if indefinite metric spaces are considered, they can be treated in the same way and are essentially the same."

"This versatile book teaches control system design using H∞infty techniques that are simple and compatible with classical control, yet powerful enough to quickly allow the solution of physically meaningful problems. The authors begin by teaching how to formulate control system design problems as mathematical optimization problems and then discuss the theory and numerics for these optimization problems. Their approach is simple and direct, and since the book is modular, the parts on theory can be read independently of the design parts and vice versa, allowing readers to enjoy the book on many levels.The development of H∞infty engineering was one of the main accomplishments of control in the 1980s. However, until now, there has not been a publication suitable for teaching the topic at the undergraduate level. This book fills that gap by teaching control system design using H∞infty techniques at a level within reach of the typical engineering and mathematics student. It also contains a readable account of recent developments and mathematical connections.The authors treat control design problems in a physically correct way. They present a small set of specific rules that the reader can apply to convert a particular design problem to the fundamental optimization problem of H∞infty control. This precisely formulated mathematics problem can then be solved on a computer. The book introduces the control software package OPTDesign, which allows the reader to easily reproduce the calculations done in the solved examples and even try variations on them. The description of how to convert an engineering problem to a form suitable for CAD is simpler than in other books."

"One of the main accomplishments of control in the 1980s was the development of H∞ techniques. This book teaches control system design using H∞ methods. Students will find this book easy to use because it is conceptually simple. They will find it useful because of the widespread appeal of classical frequency domain methods.Classical control has always been presented as trial and error applied to specific cases; Helton and Merino provide a much more precise approach. This has the tremendous advantage of converting an engineering problem to one that can be put directly into a mathematical optimization package.After completing this course, students will be familiar with how engineering specs are coded as precise mathematical constraints."

"H∞ control originated from an effort to codify classical control methods, where one shapes frequency response functions for linear systems to meet certain objectives. H∞ control underwent tremendous development in the 1980s and made considerable strides toward systematizing classical control. This book addresses the next major issue of how this extends to nonlinear systems.At the core of nonlinear control theory lie two partial differential equations (PDEs). One is a first-order evolution equation called the information state equation, which constitutes the dynamics of the controller. One can view this equation as a nonlinear dynamical system. Much of this volume is concerned with basic properties of this system, such as the nature of trajectories, stability, and, most important, how it leads to a general solution of the nonlinear H∞ control problem.The second PDE actually builds on a classical type of partial differential inequality (PDI) called a Bellman-Isaacs inequality. While the information state PDE determines the dynamics of the controller, the PDI determines the output of the controller. The authors explore the system theoretic significance of the PDI and present its gross structure. These equations are only a few years old and their study is an expanding area of research.This book also emphasizes the theory effecting computer solvability of the information state equation, which at the outset looks numerically intractable, but which surprisingly is in many cases tractable. For example, the theory shows that careful initialization has a major influence on computer solvability.The authors keep the book self-contained by using the appendices to help explain certain prerequisite material. The reader should have a basic knowledge of control theory, real analysis and differential equations, nonlinear operator theory, and nonlinear PDEs."

"Uncertainty and risk are integral to engineering because real systems have inherent ambiguities that arise naturally or due to our inability to model complex physics. The authors discuss probability theory, stochastic processes, estimation, and stochastic control strategies and show how probability can be used to model uncertainty in control and estimation problems. The material is practical and rich in research opportunities.The authors provide a comprehensive treatment of stochastic systems from the foundations of probability to stochastic optimal control. The book covers discrete- and continuous-time stochastic dynamic systems leading to the derivation of the Kalman filter, its properties, and its relation to the frequency domain Wiener filter as well as the dynamic programming derivation of the linear quadratic Gaussian (LQG) and the linear exponential Gaussian (LEG) controllers and their relation to H2 and H controllers and system robustness.Stochastic Processes, Estimation, and Control is divided into three related sections. First, the authors present the concepts of probability theory, random variables, and stochastic processes, which lead to the topics of expectation, conditional expectation, and discrete-time estimation and the Kalman filter. After establishing this foundation, stochastic calculus and continuous-time estimation are introduced. Finally, dynamic programming for both discrete-time and continuous-time systems leads to the solution of optimal stochastic control problems, resulting in controllers with significant practical application."

"Risiko operasional merupakan salah satu jenis risiko pada perbankan yang wajib dikelola dengan baik karena sifatnya yang melekat pada setiap aktifitas fungsional bank. Dalam pengelolaan risiko operasional, bank dipersyaratkan untuk memperhitungkan kerugian yang diperkirakan dan kerugian yang tidak diperkirakan dalam kebutuhan modal bagi risiko operasional. Kebutuhan modal bagi risiko operasional ini dikenal sebagai Economic Capital (EC). Komite Basel dalam aturan Basel II, memberikan tiga pendekatan dalam perhitungan EC salah satunya pendekatan Advanced Measurement Approach (AMA). Metode AMA yang banyak digunakan adalah metode Loss Distribution Approach (LDA). Dalam metode LDA, bank harus mengestimasi loss severity distribution (distribusi severitas) dan loss frequency distribution (distribusi frekuensi) kemudian membentuk aggregate loss distribution dari gabungan kedua distribusi tersebut. Nilai EC dengan metode LDA didapat dari Value at Risk (VaR) pada aggregate loss distribution dengan tingkat kepercayaan 99,9%. Permasalahan dari metode LDA saat ini adalah dalam mengestimasi distribusi severitas masih berbasis pada suatu model distribusi tertentu, padahal banyak kasus dimana data tidak dapat digambarkan dengan baik oleh suatu model distribusi yang sudah ada. Oleh karena itu, dalam tulisan ini akan dijelaskan solusi dari permasalahan tersebut, yaitu dengan mengestimasi distribusi severitas berbasis pada data. Metode yang digunakan adalah Kernel Density Estimation (KDE). KDE merupakan suatu pendekatan statistika non-parametrik untuk mengestimasi fungsi distribusi probabilitas dari suatu variabel acak jika diasumsikan bentuk atau model distribusi dari variabel acak tersebut tidak diketahui. Hasil dari penelitian adalah estimasi distribusi severitas oleh KDE lebih baik dalam menggambarkan data dibandingkan dengan menggunakan model distribusi tertentu. Nilai EC yang dihasilkan oleh metode LDA yang menggunakan KDE lebih kecil 1,6 – 3,2% dibandingkan nilai EC yang dihasilkan oleh metode LDA yang menggunakan model distribusi tertentu.

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Operational risk is one kind of risk on banking which must be managed well because of its character is inherent in every fungtional activity in Bank. In the management of operasional risk, Bank must be able to calculate a predictable loss and an unpredictable loss in capital requisite for operasional risk. The capital requisite in operasional risk is known as Economic Capital (EC). In the regulation of Basel II, Committee Basel gives three approaches of calculation in EC. One of that is Advanced Measurement Approach (AMA). In AMA method that is the most used in approach is Loss Distribution Approach (LDA) method. In LDA method, Bank must be able to estimate loss severity distribution (severity distribution) and loss frequency distribution (frequency distribution) and aggregate loss distribution is formed from both of them. Through LDA method, the value at EC can be gotten from Value at Risk (VaR) in aggregate loss distribution with the level of confidence reaches 99,9%. The problem from LDA method recently is in estimation a severity distribution which is still refers to a model on particular distribution whereas there are many cases which can not describe a data well through a distribution model that has been there. Therefore, in this paper, it will be explained how to face or the good solution from that problem. The good solution to face it is through estimation severity distribution that is refers to the data with using Kernel Density Estimation (KDE) method. KDE is a statistic approach non- parametric to estimate the function of distribution from disordered variabel that has not known. The result on this research is estimation of severity distribution through KDE is better than another in describing the data. LDA method using KDE is smaller the value at EC 1,6 % - 3,2 % than the value at EC using another distribution model in LDA method."