Predictive models to study neuromuscular control of walking in older people. This project aims to address a major challenge in human motion simulation: to deliver computationally-efficient predictive simulations of movement biomechanics. It plans to bring together the latest developments in computational modelling, medical imaging and nonlinear optimal control theory to advance current understanding of how individual lower-limb muscles stabilise and control body movement during locomotion in hea ....Predictive models to study neuromuscular control of walking in older people. This project aims to address a major challenge in human motion simulation: to deliver computationally-efficient predictive simulations of movement biomechanics. It plans to bring together the latest developments in computational modelling, medical imaging and nonlinear optimal control theory to advance current understanding of how individual lower-limb muscles stabilise and control body movement during locomotion in healthy young and older adults. New knowledge of how age-related changes in muscle mechanical properties affect the neuromuscular control of walking may assist in the design of more targeted exercise-based therapies aimed at maintaining independent function and improving the quality of life for older adults.Read moreRead less
Queueing systems and their application to telecommunication systems and dams. The aim of this project is to investigate the behaviour of large queueing systems under critical load conditions and solve problems related to large telecommunication systems, information technologies and dams. The project will have significant economic and social benefits. It will lead to the solution of high priority problems of optimal control of water resources, as well as problems in design technology of high spee ....Queueing systems and their application to telecommunication systems and dams. The aim of this project is to investigate the behaviour of large queueing systems under critical load conditions and solve problems related to large telecommunication systems, information technologies and dams. The project will have significant economic and social benefits. It will lead to the solution of high priority problems of optimal control of water resources, as well as problems in design technology of high speed telecommunication networks. It will suggest new more profitable approaches to known problems such as effective bandwidth problem, analysis and design of computer networks, optimal control of dams, and anticipate not ordinary results and solutions. It will contribute to the mathematical culture in Australia and worldwide. Read moreRead less
Renewable energy generation from flow-induced vibration. Much engineering effort has been expended to eliminate vibration of marine structures. This project seeks to provide the basis for the development of tidal energy harnessing, by deliberately amplifying and harnessing vibration. This technology offers the promise of capturing clean, zero-emissions energy, while presenting no risk to marine life.
Design of Real-time Optimisation Methods with Guaranteed Performance. The project aim is the development of a framework for the advancement of optimisation algorithms operating in real-time applications. This project expects to generate new knowledge in the area of systems theory and optimisation, and its application to time-varying problems. Expected outcomes of this project should lead to a new theoretical and practical framework that aims to ameliorate the shortcomings of the existing approac ....Design of Real-time Optimisation Methods with Guaranteed Performance. The project aim is the development of a framework for the advancement of optimisation algorithms operating in real-time applications. This project expects to generate new knowledge in the area of systems theory and optimisation, and its application to time-varying problems. Expected outcomes of this project should lead to a new theoretical and practical framework that aims to ameliorate the shortcomings of the existing approaches that struggle to rapidly respond to new information. This should provide significant benefits. Specifically, this project aims to facilitate a technological leap that generates smaller, faster, and more powerful embedded systems such as broadband services, mobile phones, medical imagining, radar and avionics.Read moreRead less
Digitally networked dynamical systems: Performance and robustness analysis. The project aim is to advance mathematical and computational tools for analyzing collections of dynamical systems that interact with each other by the digital exchange of information. The significance of this aim stems from the emergence and growing complexity and scale of such cyber-physical networks in diverse domains, including agriculture, manufacturing, transport, and infrastructure management. The expected outcomes ....Digitally networked dynamical systems: Performance and robustness analysis. The project aim is to advance mathematical and computational tools for analyzing collections of dynamical systems that interact with each other by the digital exchange of information. The significance of this aim stems from the emergence and growing complexity and scale of such cyber-physical networks in diverse domains, including agriculture, manufacturing, transport, and infrastructure management. The expected outcomes will broaden the scope for exploring achievable performance in the design and deployment of systems that leverage networked interaction for operational gains. Beyond the technical advances, benefits will include sustaining Australia's strong reputation in systems engineering research and researcher training in this area.Read moreRead less
Optimisation Geometry. Signal processing is an enabling technology for multi-billion dollar industries including broadband connections, medical imaging devices and automotive collision avoidance systems. A key component is real-time optimisation. While various aspects of real-time optimisation have been studied extensively, especially under the banner of adaptive signal processing, the general (non-adaptive) problem will be studied here from a geometric viewpoint. Morse theory and other tools fr ....Optimisation Geometry. Signal processing is an enabling technology for multi-billion dollar industries including broadband connections, medical imaging devices and automotive collision avoidance systems. A key component is real-time optimisation. While various aspects of real-time optimisation have been studied extensively, especially under the banner of adaptive signal processing, the general (non-adaptive) problem will be studied here from a geometric viewpoint. Morse theory and other tools from differential topology will be used to understand the inherent complexity of real-time optimisation problems and to develop novel numerical algorithms for classes of real-time optimisation problems having widespread applicability.Read moreRead less
Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concr ....Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concrete applications. This project should contribute to the development of the mathematical theory and give insight for concrete applications in physics and biology.Read moreRead less
Stability of Generalised Equations and Variational Systems. This project seeks to advance a new mathematical theory of variational analysis which may lead to applications in optimisation. The emphasis will be on extensions of regularity concepts appropriate for studying stability (the ‘radius of good behaviour’) of solutions to optimisation problems, particularly those of semi-infinite optimisation and programs with equilibrium constraints, when standard assumptions are not satisfied. The expect ....Stability of Generalised Equations and Variational Systems. This project seeks to advance a new mathematical theory of variational analysis which may lead to applications in optimisation. The emphasis will be on extensions of regularity concepts appropriate for studying stability (the ‘radius of good behaviour’) of solutions to optimisation problems, particularly those of semi-infinite optimisation and programs with equilibrium constraints, when standard assumptions are not satisfied. The expected outcomes may have an impact in enhancing the convergence of numerical methods and facilitating the post-optimal analysis of solutions. It may also generate new tools for increasing efficiencies and cost reductions in engineering, logistics, economics, financial systems, and environmental science.Read moreRead less
Structured barrier and penalty functions in infinite dimensional optimisation and analysis. Very large scale tightly-constrained optimisation problems are ubiquitous and include water management, traffic flow, and imaging at telescopes and hospitals. Massively parallel computers can solve such problems and provide physically realisable solution only if subtle design issues are mastered. Resolving such issues is the goal of this project.
A stochastic geometric framework for Bayesian sensor array processing. This project develops a mathematical framework, and a new generation of techniques, for sensor array processing to address real-world problems with uncertainty in array parameters and number of signals. The outcomes will enhance the capability of sensors in many application areas including, radar, sonar, astronomy and wireless communications.