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

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

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 paper develops a guidance law for a small unmanned aerial vehicle (UAV) performing vision-based tracking of a target moving on the ground. The target’s velocity is unknown, but constant; the relative altitude between the target and the UAV is also assumed to be unknown and constant. This work extends earlier results for which the relative altitude between the target and the UAV was known, for example, by comparing captured images with a geo-referenced database. The problem of estimating the unknown parameters is addressed using an adaptive estimator that uses real-time measurements of the target position in the camera frame, as provided by an image processing algorithm. The parameter estimates are used in the UAV guidance law, with turn rate as the input, where the objective is to maintain a desired horizontal distance between the UAV and the target. Simulations show that the proposed algorithm is eective at tracking a target moving with unknown constant velocity, even with repeated out-of-frame events. A stability proof for the combined estimation and guidance algorithm is provided. The paper also describes the development of a Hardware-in-the-Loop simulation, reflecting a realistic tactical scenario, that is intended to provide further validation in advance of flight tests.

Development of a vision-based guidance law for tracking a moving target

A decentralized adaptive control design procedure for large-scale uncertain systems is developed using Single Hidden Layer neural networks. The subsystems are assumed to be feedback linearizable and non-affine in the control, and their interconnections bounded linearly by the tracking error norms. Single Hidden Layer neural networks are introduced to approximate the feedback linearization error signal online from available measurements. A robust adaptive signal is required in the analysis to shield the feedback linearizing control law from the interconnection effects. The tracking errors are shown to be uniformly ultimately bounded, and all other signals uniformly bounded. The proposed adaptive algorithm is implemented in simulation to stabilize an interconnected double inverted pendulum.

Naira Hovakimyan

Papers

Development of a vision-based guidance law for tracking a moving target

Decentralized control of large-scale systems using single hidden layer neural networks

Time-Critical Cooperative Control of Autonomous Air Vehicles

Adaptive control laws for flexible semi-span wind tunnel model of high-aspect ratio flying wing

L1 Adaptive Controller for Uncertain Nonlinear Multi-Input Multi-Output Systems with Input Quantization