High-Speed and Low-Cost Implementation of Explicit Model Predictive Controllers

This paper presents a new form of piecewise-affine (PWA) solution, referred to as PWA hierarchical (PWAH), to approximate the explicit model predictive control (MPC) law, achieving a very rapid control response with the use of very few computational and memory resources. This is possible because PWAH controllers consist of single-input single-output PWA modules connected in cascade so that the parameters needed to define them increase linearly instead of exponentially with the input dimension of the control problem. PWAH controllers are not universal approximators but several explicit MPC controllers can be efficiently approximated by them. A methodology to design PWAH controllers is presented and validated with application examples already solved by MPC approaches. The designed PWAH controllers implemented in field-programmable gate arrays provide the highest control speed using the fewest resources compared with the other digital implementations reported in the literature.Ministerio de Economía, Industria y Competitividad TEC2014-57971-

Implementation and Applications of Logarithmic Signal Processing on an FPGA

This thesis presents two novel algorithms for converting a normalised binary floating point number into a binary logarithmic number with the single-precision of a floating point number. The thesis highlights the importance of logarithmic number systems in real-time DSP applications. A real-time cross-correlation application where logarithmic signal processing is used to simplify the complex computation is presented. The first algorithm presented in this thesis comprises two stages. A piecewise linear approximation to the original logarithmic curve is performed in the first stage and a scaled-down normalised error curve is stored in the second stage. The algorithm requires less than 20 kbits of ROM and a maximum of three small multipliers. The architecture is implemented on Xilinx's Spartan3 and Spartan6 FPGA family. Synthesis results confirm that the algorithm operates at a frequency of 42.3 MHz on a Spartan3 device and 127.8 MHz on a Spartan6. Both solutions have a pipeline latency of two clocks. The operating speed increases to 71.4 MHz and 160 MHz respectively when the pipeline latencies increase to eight clocks. The proposed algorithm is further improved by using a PWL (Piece-Wise Linear) approximation of the transform curve combined with a PWL approximation of a scaled version of the normalized segment error. A hardware approach for reducing the memory with additional XOR gates in the second stage is also presented. The architecture presented uses just one 18k bit Block RAM (BRAM) and synthesis results indicate operating frequencies of 93 and 110 MHz when implemented on the Xilinx Spartan3 and Spartan6 devices respectively. Finally a novel prototype of an FPGA-based four channel correlation velocimetry system is presented. The system operates at a higher sampling frquency than previous published work and outputs the new result after every new sample it receives. The system works at a sampling frequency of 195.31 kHz and a sample resolution of 12 bits. The prototype system calculates a delay in a range of 0 to 2.6 ms with a resolution of 5.12 us

Security Analysis of Order Preserving Symmetric Cryptography”,

Abstract: Order preserving encryption is a type of homomorphic encryption in which the homomorphic operation is order comparison. This means that comparing encrypted data returns the same result than comparing the original data. This allows to order encrypted data without the need of decryption. A possible use for this kind of cryptosystems is in databases, where a record field may be encrypted and still permit range queries. An important problem is determining how good a particular order preserving encryption scheme is. In fact, characteristics of order preserving cryptosystems make traditional security analysis useless. In this paper, we propose two different methodologies, applicable to most order preserving schemes, that can be used to determine their security by analyzing their randomness. The first one relies on techniques of noise analysis by converting the encryption function into a noise signal whose power distribution will be considered. The second one relies on techniques of error analysis. It is based on the computation of the mean absolute errors between the encryption function and several approximations defined by small sets of plaintext-ciphertext pairs. As a derived result of the first of these methodologies, a new order preserving cryptosystem is proposed

Similarity Queries for Temporal Toxicogenomic Expression Profiles

We present an approach for answering similarity queries about gene expression time series that is motivated by the task of characterizing the potential toxicity of various chemicals. Our approach involves two key aspects. First, our method employs a novel alignment algorithm based on time warping. Our time warping algorithm has several advantages over previous approaches. It allows the user to impose fairly strong biases on the form that the alignments can take, and it permits a type of local alignment in which the entirety of only one series has to be aligned. Second, our method employs a relaxed spline interpolation to predict expression responses for unmeasured time points, such that the spline does not necessarily exactly fit every observed point. We evaluate our approach using expression time series from the Edge toxicology database. Our experiments show the value of using spline representations for sparse time series. More significantly, they show that our time warping method provides more accurate alignments and classifications than previous standard alignment methods for time series

Video data modulation study, volume 1 Final report

Video data modulation technique

Calculus Unlimited

Purpose: This book is intended to supplement our text, Calculus (Benjamin/Cummings, 1980), or virtually any other calculus text (see page vii, How To Use This Book With Your Calculus Text). As the title Calculus Unlimited implies, this text presents an alternative treatment of calculus using the method of exhaustion for the derivative and integral in place of limits. With the aid of this method, a definition of the derivative may be introduced in the first lecture of a calculus course for students who are familiar with functions and graphs. Approach: Assuming an intuitive understanding of real numbers, we begin in Chapter 1 with the definition of the derivative. The axioms for real numbers are presented only when needed, in the discussion of continuity. Apart from this, the development is rigorous and contains complete proofs. As you will note, this text has a more geometric flavor than the usual analytic treatment of calculus. For example, our definition of completeness is in terms of convexity rather than least upper bounds, and Dedekind cuts are replaced by the notion of a transition point. Who Should Use This Book: This book is for calculus instructors and students interested in trying an alternative to limits. The prerequisites are a knowledge of functions, graphs, high school algebra and trigonometry. How To Use This Book: Because the "learning-by-doing" technique introduced in Calculus has proved to be successful, we have adapted the same format for this book. The solutions to "Solved Exercises" are provided at the back of the book; however readers are encouraged to try solving each example before looking up the solution. The Origin Of The Definition of The Derivative: Several years ago while reading Geometry and the Imagination, by Hilbert and Cohn-Vossen (Chelsea, 1952, p. 176), we noticed a definition of the circle of curvature for a plane curve C. No calculus, as such, was used in this definition. This suggested that the same concept could be used to define the tangent line and thus serve as a limit-free foundation for the differential calculus. We introduced this new definition of the derivative into our class notes and developed it in our calculus classes for several years. As far as we know, the definition has not appeared elsewhere. If our presumption of originality is ill-founded, we welcome your comments. Jerrold Marsden Alan Weinstein Berkeley, C

Modeling Human Mobility Entropy as a Function of Spatial and Temporal Quantizations

The knowledge of human mobility is an integral component of several different branches of research and planning, including delay tolerant network routing, cellular network planning, disease prevention, and urban planning. The uncertainty associated with a person's movement plays a central role in movement predictability studies. The uncertainty can be quantified in a succinct manner using entropy rate, which is based on the information theoretic entropy. The entropy rate is usually calculated from past mobility traces. While the uncertainty, and therefore, the entropy rate depend on the human behavior, the entropy rate is not invariant to spatial resolution and sampling interval employed to collect mobility traces. The entropy rate of a person is a manifestation of the observable features in the person's mobility traces. Like entropy rate, these features are also dependent on spatio-temporal quantization. Different mobility studies are carried out using different spatio-temporal quantization, which can obscure the behavioral differences of the study populations. But these behavioral differences are important for population-specific planning. The goal of dissertation is to develop a theoretical model that will address this shortcoming of mobility studies by separating parameters pertaining to human behavior from the spatial and temporal parameters

Calculus I

Preface: The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition...