Monge-Ampere equations and applications. The Monge-Ampere equation is a premier fully nonlinear partial differential equation with significant applications in geometry, physics and applied science. Building upon breakthroughs made by the proposers in previous grant research, this project aims to resolve challenging problems involving Monge-Ampere type equations and applications. The project goal is to establish new regularity theory and classify singularity profile for solutions to Monge-Ampere ....Monge-Ampere equations and applications. The Monge-Ampere equation is a premier fully nonlinear partial differential equation with significant applications in geometry, physics and applied science. Building upon breakthroughs made by the proposers in previous grant research, this project aims to resolve challenging problems involving Monge-Ampere type equations and applications. The project goal is to establish new regularity theory and classify singularity profile for solutions to Monge-Ampere type equation arising in applied sciences, by introducing new ideas and developing innovative cutting-edge techniques. Expected outcomes include resolution of outstanding open problems and continuing enhancement of Australian leadership and expertise in a major area of mathematics.
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Uncertainty in the social cost of carbon dioxide: control theoretic methods. This project aims to redevelop the most commonly used social cost of carbon dioxide (SC-CO2) modeling framework using the best available scientific data and state-of-the-art uncertainty quantification techniques, providing government and industry decision-makers with a robust tool to tackle a carbon-constrained future. This project will deliver improved, robust estimates of the SC-CO2, a proxy for a price on carbon emis ....Uncertainty in the social cost of carbon dioxide: control theoretic methods. This project aims to redevelop the most commonly used social cost of carbon dioxide (SC-CO2) modeling framework using the best available scientific data and state-of-the-art uncertainty quantification techniques, providing government and industry decision-makers with a robust tool to tackle a carbon-constrained future. This project will deliver improved, robust estimates of the SC-CO2, a proxy for a price on carbon emissions that is used by governments, businesses, and financial bodies. This will enable Australia to play a leading and proactive role in the international pursuit of significant and sustained reductions in greenhouse gas emissions.Read moreRead less
Safe, Plug and Play, Multi Agent Dynamic Systems. From driverless cars, to networks of nano satellites, and complex biological networks, the modern world has many examples of multi agent dynamic systems that need careful coordination and control to perform correctly. In many cases, these systems are built up using designs based on intuition, computer simulations and empirical testing. However, there is a clear need to advance the fundamental understandings of such systems: (i) Verifiable overall ....Safe, Plug and Play, Multi Agent Dynamic Systems. From driverless cars, to networks of nano satellites, and complex biological networks, the modern world has many examples of multi agent dynamic systems that need careful coordination and control to perform correctly. In many cases, these systems are built up using designs based on intuition, computer simulations and empirical testing. However, there is a clear need to advance the fundamental understandings of such systems: (i) Verifiable overall dynamic system properties need to be derived to give assurance of performance in situations not previously envisaged; (ii) It is also critical to understand stable system behaviours not just with fixed configurations, but with agile configurations such as splitting, merging, and morphingRead moreRead less
Robust Data-Driven Control for Safety-Critical Systems. This project aims to develop new approaches to controlling robotic and cyber-physical systems in safety-critical applications. This project expects to generate new knowledge in how to harness the power of machine learning for robot control, while guaranteeing safety and stability at all times. The outcomes of this project will be new algorithms and a deeper understanding of the interplay of data, learning, and models, as well as experimenta ....Robust Data-Driven Control for Safety-Critical Systems. This project aims to develop new approaches to controlling robotic and cyber-physical systems in safety-critical applications. This project expects to generate new knowledge in how to harness the power of machine learning for robot control, while guaranteeing safety and stability at all times. The outcomes of this project will be new algorithms and a deeper understanding of the interplay of data, learning, and models, as well as experimental validation on a surgical robot and a bipedal walking robot. This project will provide significant benefits by dramatically increasing the range of applications in which the power of machine learning can be safely applied to advance the capabilities and uptake of robotics.Read moreRead less
New mathematics for multi-extremal optimization and diffusion tensor imaging. This project aims to establish numerically certifiable mathematical theory and methods for semi-algebraic optimisation problems. Numerically certifiable optimisation principles and techniques are vital for the practical use of optimisation technologies because they can be readily implemented by common computer models and algorithms. Yet no such methodologies exist for multi-extremal, semi-algebraic optimisation problem ....New mathematics for multi-extremal optimization and diffusion tensor imaging. This project aims to establish numerically certifiable mathematical theory and methods for semi-algebraic optimisation problems. Numerically certifiable optimisation principles and techniques are vital for the practical use of optimisation technologies because they can be readily implemented by common computer models and algorithms. Yet no such methodologies exist for multi-extremal, semi-algebraic optimisation problems which are common in modern science and medicine. The expected outcomes of this project include enhanced optimisation methods for diffusion tensor imaging, an emerging technology in brain sciences.Read moreRead less
Innovations in sparse optimisation: big data nonsmooth optimisation. This project aims to produce innovative optimisation methods capable of solving a wide range of practical problems that are currently too complex to be solved. Optimisation involving huge data sets is ubiquitous. Sparse optimisation has emerged as a challenging frontier of modern optimisation because it effectively computes an optimal solution with desired low complexity structure so that a resulting solution can be efficiently ....Innovations in sparse optimisation: big data nonsmooth optimisation. This project aims to produce innovative optimisation methods capable of solving a wide range of practical problems that are currently too complex to be solved. Optimisation involving huge data sets is ubiquitous. Sparse optimisation has emerged as a challenging frontier of modern optimisation because it effectively computes an optimal solution with desired low complexity structure so that a resulting solution can be efficiently stored, implemented and utilised, and is robust to the data inexactness. This project aims at developing innovative mathematical techniques and efficient numerical schemes for solving sparse optimisation problems. The intended outcomes will have significant impact on many areas of science, medicine and engineering, where sparse optimisation is used, including cancer radiotherapy optimal planning.Read moreRead less
Relaxed reflection methods for feasibility and matrix completion problems. The project proposes to further develop the non-linear convergence theory, and to provide problem-specific implementations. Many applied and pure problems require solution of a large set of linear or nonlinear equations (or inequalities). Highly effective, parallelisable methods are based on iterated projection or reflection algorithms which aggregate information about individual equations. The theory is well developed in ....Relaxed reflection methods for feasibility and matrix completion problems. The project proposes to further develop the non-linear convergence theory, and to provide problem-specific implementations. Many applied and pure problems require solution of a large set of linear or nonlinear equations (or inequalities). Highly effective, parallelisable methods are based on iterated projection or reflection algorithms which aggregate information about individual equations. The theory is well developed in the linear case, but does not explain many important applications for which they are often highly successful (eg optical aberration correction, protein reconstruction, tomography, compressed sensing). The project also plans to provide heuristics to help explain why an algorithm performs well on one class of applications but fails on another.Read moreRead less
Control and learning for enhancing capabilities of quantum sensors. This project aims to develop new theories and algorithms to enhance capabilities in engineering quantum sensors from the perspective of systems and control. The project is significant because it is anticipated to advance key knowledge and provide systematic methods to enable achievement of high-precision sensing for wide applications, e.g., early disease detection, medical research, discovery of ore deposits and groundwater moni ....Control and learning for enhancing capabilities of quantum sensors. This project aims to develop new theories and algorithms to enhance capabilities in engineering quantum sensors from the perspective of systems and control. The project is significant because it is anticipated to advance key knowledge and provide systematic methods to enable achievement of high-precision sensing for wide applications, e.g., early disease detection, medical research, discovery of ore deposits and groundwater monitoring. The intended outcomes are fundamental theories, effective control and learning algorithms for achieving highly-sensitive sensors. These outcomes should make important contributions to and deliver new knowledge and skills for Australia's sensing industries, which could benefit Australia's economic growth.Read moreRead less
Robustness, resilience and security of networked dynamic systems. This project will develop advanced digital control techniques to address security, resilience and robustness in complex networks and deliver fundamental advances in the technology for secure and reliable networks. The project will advance the theory on consensus of networked multi-agent systems to facilitate the fast adoption of the internet of things and the continuous growth of cyber-physical systems These systems in many cases ....Robustness, resilience and security of networked dynamic systems. This project will develop advanced digital control techniques to address security, resilience and robustness in complex networks and deliver fundamental advances in the technology for secure and reliable networks. The project will advance the theory on consensus of networked multi-agent systems to facilitate the fast adoption of the internet of things and the continuous growth of cyber-physical systems These systems in many cases work with high efficiency, stability, and low communication overheads. However, there are cases where disturbance amplification and cascading failures can arise from relatively small unforeseen events. The theoretical work will be complemented by detailed nonlinear networked simulations, using intelligent vehicle systems as a case study.Read moreRead less
Distributed Estimation, Control and Optimisation for Networked Systems. This project aims to study large scale networked systems in major infrastructures including power networks, transportation networks, internet of things, and other cyber-physical systems. This project is expected to develop new methodology and algorithms for distributed estimation, control and optimisation of these systems. Distributed solutions are essential because traditional techniques which were designed for small system ....Distributed Estimation, Control and Optimisation for Networked Systems. This project aims to study large scale networked systems in major infrastructures including power networks, transportation networks, internet of things, and other cyber-physical systems. This project is expected to develop new methodology and algorithms for distributed estimation, control and optimisation of these systems. Distributed solutions are essential because traditional techniques which were designed for small systems are not suitable for efficient operations of large scale systems. Application examples include distributed state estimation for power networks, control of multi-agent systems and optimal scheduling of transportation networks. The outcomes of this project are vital to the understanding and management of these systems. Read moreRead less