Multiscale Singularly Perturbed Control Systems. We propose to develop a unified averaging technique to analyse deterministic and stochastic multiscale singularly perturbed control systems. Such systems arise as mathematical models of real-world dynamical systems in which state variables can change their values with the rates of different orders of magnitude. The technique is based on the assumption that the system, which would describe the dynamics of the fast state variables if slow ones were ....Multiscale Singularly Perturbed Control Systems. We propose to develop a unified averaging technique to analyse deterministic and stochastic multiscale singularly perturbed control systems. Such systems arise as mathematical models of real-world dynamical systems in which state variables can change their values with the rates of different orders of magnitude. The technique is based on the assumption that the system, which would describe the dynamics of the fast state variables if slow ones were frozen, possesses certain ergodicity properties expressed in the existence of its limit occupational measures set. Conditions for the existence of such a set will be studied and its structure will be described.Read moreRead less
Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications. We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analy ....Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications. We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analysis and asymptotic optimisation of singularly perturbed control systems and Markov decision processes. In particular, we plan to establish links between general nonlinear optimal control problems with time average criteria and linear programming problems in the space of limit occupational measures generated by the underlying control system.Read moreRead less
Efficient Processing of Complex Spatial Queries. Similarity search and join are two of the most popular yet complex queiries in spatial databases. They are also two of the major spatial data analysis paradigms. To complement the existing techniques, this project aims to investigate a more complex and important form of these two problems, and to develop novel framework to approach the proposed problems. The successful achievements of the project will not only bring new spatial data analysis techn ....Efficient Processing of Complex Spatial Queries. Similarity search and join are two of the most popular yet complex queiries in spatial databases. They are also two of the major spatial data analysis paradigms. To complement the existing techniques, this project aims to investigate a more complex and important form of these two problems, and to develop novel framework to approach the proposed problems. The successful achievements of the project will not only bring new spatial data analysis techniques but also deliever effective solutions to a number of real-life apllications.Read moreRead less
Electrodynamics of the High Latitude Ionosphere. Electrical power (~10^12 W on average), incident over the high latitude ionospheres drives auroral displays, causes magnetic disturbances and other space weather effects over the globe, including Australia. This project uses Iridium, a US$6 billion, commercial satellite constellation, to study energy deposition into the ionosphere from near-Earth space. The Iridium data is not public domain. This project provides data access, representing a signif ....Electrodynamics of the High Latitude Ionosphere. Electrical power (~10^12 W on average), incident over the high latitude ionospheres drives auroral displays, causes magnetic disturbances and other space weather effects over the globe, including Australia. This project uses Iridium, a US$6 billion, commercial satellite constellation, to study energy deposition into the ionosphere from near-Earth space. The Iridium data is not public domain. This project provides data access, representing a significant cost-effective way for Australia to participate in observational space science. Australian postgraduate training is an integral part of the project, providing international level access and interpretation of scientific satellite and over the horizon radar network data.Read moreRead less
Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and ana ....Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and analyse mathematical and statistical models for natural and artificial complex systems,
- to use these models to develop an understanding of the behaviour of these systems
- to incorporate this understanding into strategies for management and control.Read moreRead less
A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for e ....A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for efficient use. Superfractals and the associated colouring algorithm could be used to develop a new system to produce synthetic content for wireless devices that would require only low bandwidth.Read moreRead less
Optical Multiple-Input Multiple-Output Communication Systems. Optical multiple-input multiple-output (MIMO) systems exploit a simple yet powerful principle of diversity to improve the capacity and robustness of optical networks. This proposal focuses on making the most use of two polarisation modes intrinsic to the fiber by applying MIMO techniques to the optical communication systems. This project can potentially create many commercial opportunities in Australia in the area of integrated photon ....Optical Multiple-Input Multiple-Output Communication Systems. Optical multiple-input multiple-output (MIMO) systems exploit a simple yet powerful principle of diversity to improve the capacity and robustness of optical networks. This proposal focuses on making the most use of two polarisation modes intrinsic to the fiber by applying MIMO techniques to the optical communication systems. This project can potentially create many commercial opportunities in Australia in the area of integrated photonic circuits and high-speed digital signal processing. The funding support of these research activities will further enhance Australia's international ICT reputation in this emerging field.Read moreRead less
Increasing internet energy and cost efficiency by improving higher-layer protocols. Australians rely heavily on our telecommunications infrastructure due to our geographic dispersion. We are also very susceptible to climate change, given our reliance on agriculture. Information technology is consuming a rapidly increasing fraction of our power and our budget. This research will help to reverse both those trends, by finding novel and practical ways to use our infrastructure more efficiently, and ....Increasing internet energy and cost efficiency by improving higher-layer protocols. Australians rely heavily on our telecommunications infrastructure due to our geographic dispersion. We are also very susceptible to climate change, given our reliance on agriculture. Information technology is consuming a rapidly increasing fraction of our power and our budget. This research will help to reverse both those trends, by finding novel and practical ways to use our infrastructure more efficiently, and to minimise its energy use. This will enable the Australian telecommunications industry to provide better service (including to Australian industries and rural communities) at lower economic and environmental cost. This project will put Australia on the international stage as a leading contributor to energy-efficient internet technology.Read moreRead less
Analysis of Polynomial Phase Signals with Missing Observations. Many non-stationary signals in radar, physics and communications can be modelled as polynomial phase signals. These signals are often incomplete due to missing observations from intermittent sensor failures, outliers, receiver errors, periodic interference and inaccessibility of data. The aim of this project is to develop robust and computationally efficient methods for recovering such signals from small data sets when there is a la ....Analysis of Polynomial Phase Signals with Missing Observations. Many non-stationary signals in radar, physics and communications can be modelled as polynomial phase signals. These signals are often incomplete due to missing observations from intermittent sensor failures, outliers, receiver errors, periodic interference and inaccessibility of data. The aim of this project is to develop robust and computationally efficient methods for recovering such signals from small data sets when there is a large proportion of missing observations. This will contribute to a conceptual advancement in the field of signal processing and will provide new methods for use in applications such as radar, astrophysics, seismology, vibration analysis and communications.Read moreRead less
A Bayesian framework for frequency domain identification. The national and social benefits of the project will be reflected
through the application recognition of the research work in the various industry and research community; and also through our international collaboration. The national and social benefits are also delivered by producing specialized researchers and engineers in systems and control engineering. These people include the research students who will participate in and learn f ....A Bayesian framework for frequency domain identification. The national and social benefits of the project will be reflected
through the application recognition of the research work in the various industry and research community; and also through our international collaboration. The national and social benefits are also delivered by producing specialized researchers and engineers in systems and control engineering. These people include the research students who will participate in and learn from the proposed project.Read moreRead less