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

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

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Stability of Time-Delay Systems

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

Background
Recent technological advances in integrated circuits, wireless communications, and physiological sensing allow miniature, lightweight, ultra-low power, intelligent monitoring devices. A number of these devices can be integrated into a Wireless Body Area Network (WBAN), a new enabling technology for health monitoring.

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A wireless body area network of intelligent motion sensors for computer assisted physical rehabilitation

A compensation scheme is presented for general nonlinear actuator deadzones of unknown width. The compensator uses two neural networks (NNs), one to estimate the unknown deadzone and another to provide adaptive compensation in the feedforward path. The compensator NN has a special augmented form containing extra neurons whose activation functions provide a "jump function basis set" for approximating piecewise continuous functions. Rigorous proofs of closed-loop stability for the deadzone compensator are provided and yield tuning algorithms for the weights of the two NNs. The technique provides a general procedure for using NNs to determine the preinverse of an unknown right-invertible function.

Deadzone compensation in motion control systems using neural networks

From the Publisher:
About the Author
Frank L. Lewis is Associate Director for Research and Head of the Advanced Controls, Sensors, and MEMS Group at the Automation and Robotics Research Institute at the University of Texas at Arlington. Javier Campos is Linux Consultant Engineer at Montavista Software, Inc. in Irving, Texas. Rastko Selmic is DSP Systems Engineer at Signalogic, Inc. in Dallas, Texas.

Neuro-Fuzzy Control of Industrial Systems with Actuator Nonlinearities

A neural net (NN)-based actuator saturation compensation scheme for the nonlinear systems in Brunovsky canonical form is presented. The scheme that leads to stability, command following, and disturbance rejection is rigorously proved and verified using a general "pendulum type" and a robot manipulator dynamical systems. Online weights tuning law, the overall closed-loop system performance, and the boundedness of the NN weights are derived and guaranteed based on Lyapunov approach. The actuator saturation is assumed to be unknown and the saturation compensator is inserted into a feedforward path. Simulation results indicate that the proposed scheme can effectively compensate for the saturation nonlinearity in the presence of system uncertainty.

Neural network control of a class of nonlinear systems with actuator saturation

One of the most important properties of neural nets (NNs) for control purposes is the universal approximation property. Unfortunately,, this property is generally proven for continuous functions. In most real industrial control systems there are nonsmooth functions (e.g., piecewise continuous) for which approximation results in the literature are sparse. Examples include friction, deadzone, backlash, and so on. It is found that attempts to approximate piecewise continuous functions using smooth activation functions require many NN nodes and many training iterations, and still do not yield very good results. Therefore, a novel neural-network structure is given for approximation of piecewise continuous functions of the sort that appear in friction, deadzone, backlash, and other motion control actuator nonlinearities. The novel NN consists of neurons having standard sigmoid activation functions, plus some additional neurons having a special class of nonsmooth activation functions termed "jump approximation basis function." Two types of nonsmooth jump approximation basis functions are determined- a polynomial-like basis and a sigmoid-like basis. This modified NN with additional neurons having "jump approximation" activation functions can approximate any piecewise continuous function with discontinuities at a finite number of known points. Applications of the new NN structure are made to rigid-link robotic systems with friction nonlinearities. Friction is a nonlinear effect that can limit the performance of industrial control systems; it occurs in all mechanical systems and therefore is unavoidable in control systems. It can cause tracking errors, limit cycles, and other undesirable effects. Often, inexact friction compensation is used with standard adaptive techniques that require models that are linear in the unknown parameters. It is shown here how a certain class of augmented NN, capable of approximating piecewise continuous functions, can be used for friction compensation.

Neural-network approximation of piecewise continuous functions: application to friction compensation

This paper presents a dynamic model of wireless sensor networks (WSNs) and its application to sensor node fault detection. Recurrent neural networks (NNs) are used to model a sensor node, the node's dynamics, and interconnections with other sensor network nodes. An NN modeling approach is used for sensor node identification and fault detection in WSNs. The input to the NN is chosen to include previous output samples of the modeling sensor node and the current and previous output samples of neighboring sensors. The model is based on a new structure of a backpropagation-type NN. The input to the NN and the topology of the network are based on a general nonlinear sensor model. A simulation example, including a comparison to the Kalman filter method, has demonstrated the effectiveness of the proposed scheme.

Rastko R. Selmic

Papers

Deadzone compensation in motion control systems using neural networks

Neuro-Fuzzy Control of Industrial Systems with Actuator Nonlinearities

Neural network control of a class of nonlinear systems with actuator saturation

Neural-network approximation of piecewise continuous functions: application to friction compensation

Wireless Sensor Network Modeling Using Modified Recurrent Neural Networks: Application to Fault Detection