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
Control of network systems with signed dynamical interconnections. New technologies such as online recommendations, smart grids, and cyber-physical systems are becoming backbone infrastructure. Such systems are operated as network systems with interconnected functioning units (agents) where cooperative and adversarial agent relations often coexist. This project aims to develop the theories and tools for designing and building dynamic networks with signed interactions that arise from a variety of ....Control of network systems with signed dynamical interconnections. New technologies such as online recommendations, smart grids, and cyber-physical systems are becoming backbone infrastructure. Such systems are operated as network systems with interconnected functioning units (agents) where cooperative and adversarial agent relations often coexist. This project aims to develop the theories and tools for designing and building dynamic networks with signed interactions that arise from a variety of applications where both cooperative and adversarial agent interactions coexist. By developing theories and algorithms for control and identification over such systems, this project will contribute directly to their safe and robust operation. The resulting theories will provide deeper understanding of network control systems and the resulting algorithms will enable the elimination of attackers and malicious users for online review systems and smart grids. This project will contribute to increased cybersecurity for all Australians.Read moreRead less
Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and ....Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and the economy. This project expects to bring about long-term impact on quantitative finance and related applications through providing a deep understanding of, and a new perspective for, the design, risk and fairness of the finance, property and insurance markets.Read moreRead less
When stabilization and optimization meet: a codesign approach. The next generation of engineered systems need to perform complex tasks with precision, and be robust, resilient and adaptive to their environment enabled by the confluence of control, optimization, learning and computation Understanding the interplay between robust stability and optimization is key to this endeavor. Many techniques, such as model predictive control and reinforcement learning, rely on an intricate interplay between ....When stabilization and optimization meet: a codesign approach. The next generation of engineered systems need to perform complex tasks with precision, and be robust, resilient and adaptive to their environment enabled by the confluence of control, optimization, learning and computation Understanding the interplay between robust stability and optimization is key to this endeavor. Many techniques, such as model predictive control and reinforcement learning, rely on an intricate interplay between an optimization-based control algorithm and an optimization routine used to calculate the control law. This project aims to develop a general design framework for stability, suboptimality and robustness of such algorithms, that can be used in range of novel applications, such as driverless cars and drones. 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
Robust learning of dynamic systems. Robots and other autonomous machines use models of the real world to predict the result of their actions and make decisions, but existing methods used for machine-learning are unreliable in many cases and can be easily fooled. This project aims to make machine-learning of dynamic system models reliable, accurate, and secure. The outcomes of this project will be new models and algorithms that ensure safety and increase accuracy of models learned from data. This ....Robust learning of dynamic systems. Robots and other autonomous machines use models of the real world to predict the result of their actions and make decisions, but existing methods used for machine-learning are unreliable in many cases and can be easily fooled. This project aims to make machine-learning of dynamic system models reliable, accurate, and secure. The outcomes of this project will be new models and algorithms that ensure safety and increase accuracy of models learned from data. This project will benefit robotics, control engineering, infrastructure automation, and other fields that demand the capability to model physical systems from limited data. It will also improve cybersecurity by making learning algorithms resilient to deliberate attacks with false data.Read moreRead less
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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Australian Laureate Fellowships - Grant ID: FL190100081
Funder
Australian Research Council
Funding Amount
$3,532,919.00
Summary
Minimal surfaces, free boundaries and partial differential equations. This project enhances Australia as a world leader in the field of mathematical analysis, focusing on regularity and qualitative properties of solutions of partial differential equations and nonlocal problems, and solving very challenging research questions in a key strategic area of international science.
The broad applicability of the results constitutes a very fertile ground for cross-disciplinary interactions with scientist ....Minimal surfaces, free boundaries and partial differential equations. This project enhances Australia as a world leader in the field of mathematical analysis, focusing on regularity and qualitative properties of solutions of partial differential equations and nonlocal problems, and solving very challenging research questions in a key strategic area of international science.
The broad applicability of the results constitutes a very fertile ground for cross-disciplinary interactions with scientists of other disciplines.
A new research team based in Western Australia will be founded, connecting world leaders and talented early career researchers, providing an ideal training environment for students and PostDocs, offering an excellent image of the scientific community and developing strategic fields of knowledge.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
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