New System Identification Techniques Utilising Misspecified Models. National benefits of the proposed research project will result from improvements in control due to a better, more complete understanding of the models obtained by the newly proposed system identification technique. The resulting effect on industrial practice will be an increase in efficiency, by reduced waste, lower pollution levels and increased throughput. Also, the techniques developed will be directly applicable to current r ....New System Identification Techniques Utilising Misspecified Models. National benefits of the proposed research project will result from improvements in control due to a better, more complete understanding of the models obtained by the newly proposed system identification technique. The resulting effect on industrial practice will be an increase in efficiency, by reduced waste, lower pollution levels and increased throughput. Also, the techniques developed will be directly applicable to current research in the areas of complex systems, such as smart structures and biological studies of the dynamic effects of drugs and hormones on genes.Read moreRead less
Robust Experiment Design for Dynamical System Identification. Innovative and new robust experiment design methodologies are a Frontier Technology for Transforming Australian Industries. By providing a solid foundation for generating high fidelity models, robust experiment design will, by the use of breakthrough science, facilitate the estimation of models in minimum time. Also, this will entail minimal disruption to the normal operation of the process under study. With the majority of advanced ....Robust Experiment Design for Dynamical System Identification. Innovative and new robust experiment design methodologies are a Frontier Technology for Transforming Australian Industries. By providing a solid foundation for generating high fidelity models, robust experiment design will, by the use of breakthrough science, facilitate the estimation of models in minimum time. Also, this will entail minimal disruption to the normal operation of the process under study. With the majority of advanced industrial process control systems reliant on accurate models significant savings could also be made due to the implicit improvement in process control.Read moreRead less
New research directions in the area of sampled-data systems. Increased application of digital technology in a wide variety of control engineering applications has led to renewed interest in the study of sampled-data systems. With many applications ranging from nano-technology through to aerospace, robotics, bio-medicine and telecommunications, sampled-data systems form an integral part of many frontier technologies arising in engineering. In exploring and furthering these emerging technologies, ....New research directions in the area of sampled-data systems. Increased application of digital technology in a wide variety of control engineering applications has led to renewed interest in the study of sampled-data systems. With many applications ranging from nano-technology through to aerospace, robotics, bio-medicine and telecommunications, sampled-data systems form an integral part of many frontier technologies arising in engineering. In exploring and furthering these emerging technologies, this proposal aims to provide exciting breakthroughs in the theory of time and event driven sampled-data nonlinear systems. Equipped with these powerful new tools, we will address important analysis and design issues in this area, for example, for Networked Control Systems.Read moreRead less
Structure and states of operator-algebraic dynamical systems. This project is in the general area of functional analysis, and more specifically operator theory, an area in which the University of Wollongong has an active research group and a strong international reputation. The investigators will study dynamical systems arising in combinatorial and number-theoretic situations, where the analogue of the "dynamics'' is provided by an action of the real line on an operator algebra. Thus the project ....Structure and states of operator-algebraic dynamical systems. This project is in the general area of functional analysis, and more specifically operator theory, an area in which the University of Wollongong has an active research group and a strong international reputation. The investigators will study dynamical systems arising in combinatorial and number-theoretic situations, where the analogue of the "dynamics'' is provided by an action of the real line on an operator algebra. Thus the project will involve ideas and techniques from a wide range of mathematical disciplines, and will help to broaden Australia's expertise across these disciplines.Read moreRead less
Endomorphisms, transfer operators and Hilbert modules. This project is in the general area of functional analysis, an area where both Newcastle University and the University of New South Wales have strong international reputations. The aim of the project is to study irreversible dynamics in the presence of transfer operators, as recently introduced by Professor Exel. The motivation comes from a variety of examples arising in different areas of mathematics, including number theory and graph theor ....Endomorphisms, transfer operators and Hilbert modules. This project is in the general area of functional analysis, an area where both Newcastle University and the University of New South Wales have strong international reputations. The aim of the project is to study irreversible dynamics in the presence of transfer operators, as recently introduced by Professor Exel. The motivation comes from a variety of examples arising in different areas of mathematics, including number theory and graph theory. It is hoped that the results will give new understanding of the algebraic and analytic structure underlying the multi-resolution analyses used in approximation theory and Fourier analysis. This project will help ensure that Australia has a strong foundation in mathematics which will foster innovation.Read moreRead less
Representations of dynamical systems, amenability, and proper actions. Mathematicians study abstract objects by representing them in terms of well-understood concrete models, and need to know when a representation is faithful, in the sense that the model contains complete information. Dynamical systems are an abstraction of physical systems suitable for studying time evolution and symmetries. The project aims to determine when important representations of dynamical systems are faithful, or, in ....Representations of dynamical systems, amenability, and proper actions. Mathematicians study abstract objects by representing them in terms of well-understood concrete models, and need to know when a representation is faithful, in the sense that the model contains complete information. Dynamical systems are an abstraction of physical systems suitable for studying time evolution and symmetries. The project aims to determine when important representations of dynamical systems are faithful, or, in mathematical language, when the dynamical system is amenable. The proposed strategy involves extending Rieffel's notion of proper actions; the construction should be of wide applicability apart from the intended applications to amenability.Read moreRead less
Operator algebras associated to semigroups and graphs. This project aims to unify ideas from two highly topical areas of mathematics in which one studies discrete objects by representing them as families of linear transformations. In the first area, one represents the semigroups which model irreversible dynamics as isometries (that is, distance-preserving transformations); in the second, one represents networks by families of partially defined isometries in a way which reflects the behaviour of ....Operator algebras associated to semigroups and graphs. This project aims to unify ideas from two highly topical areas of mathematics in which one studies discrete objects by representing them as families of linear transformations. In the first area, one represents the semigroups which model irreversible dynamics as isometries (that is, distance-preserving transformations); in the second, one represents networks by families of partially defined isometries in a way which reflects the behaviour of paths in the network. The link will be achieved by viewing the operator algebras they generate as semidirect products which have been twisted by a noncommutative cocycle.Read moreRead less
The structure of quantum groups. We propose to study the structure of mathematical objects used in describing symmetries of micro-scale phenomena. The project will significantly develop already well established Australian-Korean cooperation in this exciting and rapidly growing area of research. The results will be immediately applicable to related fields of mathematics, most notably to noncommutative geometry. In the long run, the outcomes will help in better understanding of fundamental problem ....The structure of quantum groups. We propose to study the structure of mathematical objects used in describing symmetries of micro-scale phenomena. The project will significantly develop already well established Australian-Korean cooperation in this exciting and rapidly growing area of research. The results will be immediately applicable to related fields of mathematics, most notably to noncommutative geometry. In the long run, the outcomes will help in better understanding of fundamental problems of modern quantum physics.Read moreRead less
Operator algebras associated to groupoids. Australian researchers have a strong reputation for excellence and innovation in the field of operator algebras. Operator algebras associated to groupoids have been immensely influential in recent decades, both within mathematics and via applications to theoretical physics. This project will develop an innovative approach to groupoid algebras, and will help to maintain the high standing of Australian researchers in this important field.
Co-universal operator algebras. Australian researchers have established themselves at the very forefront of research into operator algebras associated to graphs. The proposed research will make an important impact, at a fundamental level, on the way that researchers around the world view these operator algebras. This will help to further strengthen Australia's reputation in this field. The proposed program will also train two PhD students in a very active area of mathematics and put them in cont ....Co-universal operator algebras. Australian researchers have established themselves at the very forefront of research into operator algebras associated to graphs. The proposed research will make an important impact, at a fundamental level, on the way that researchers around the world view these operator algebras. This will help to further strengthen Australia's reputation in this field. The proposed program will also train two PhD students in a very active area of mathematics and put them in contact with a vibrant research community. This will help contribute to the strong future of pure mathematics in Australia.Read moreRead less