Explicit methods in number theory: Computation, theory and application. This project aims to use explicit estimates to unify three problems in number theory: primitive roots, Diophantine quintuples, and linear independence of zeroes of the Riemann zeta-function. It will use computational and analytic number theory to reduce the quintuples problem to a soluble level. Pursuing relations between the zeta zeroes will overhaul many current results. This project will apply its findings about primitive ....Explicit methods in number theory: Computation, theory and application. This project aims to use explicit estimates to unify three problems in number theory: primitive roots, Diophantine quintuples, and linear independence of zeroes of the Riemann zeta-function. It will use computational and analytic number theory to reduce the quintuples problem to a soluble level. Pursuing relations between the zeta zeroes will overhaul many current results. This project will apply its findings about primitive roots to signal processing, cryptography and cybersecurity.Read 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
Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelec ....Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelectric sensor technology. Expected outcomes include manufactured proof-of-concept sensors that enable measurement of local stress fields. This should provide significant benefits, such as improved future robot capability and reliability, and research training for next-generation Australian computational mathematicians. Read moreRead less
Generalised Energy Based Robust and Nonlinear Control Systems. This project aims to develop new energy-based theories of robust stability analysis and controller design for both linear and nonlinear systems, building on passivity and negative imaginary system theories and their physical interpretations along with stochastic optimal control theory. These control theories would allow for a wide range of plant dynamics in the design of high-performance robust control systems, enabling advances in e ....Generalised Energy Based Robust and Nonlinear Control Systems. This project aims to develop new energy-based theories of robust stability analysis and controller design for both linear and nonlinear systems, building on passivity and negative imaginary system theories and their physical interpretations along with stochastic optimal control theory. These control theories would allow for a wide range of plant dynamics in the design of high-performance robust control systems, enabling advances in emerging technologies including nanopositioning, micro-electromechanical systems and opto-mechatronics. The project plans to combine these theoretical advances with numerical methods involving advanced optimisation tools and the experimental implementation of nanopositioning control systems in atomic force microscopy.Read moreRead less
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
Sensing a complex world: Infinite dimensional observer theory for robots. This project aims to develop the foundational theory and design paradigms to support the new generation of sensor systems crucial to enabling widespread robotic automation in unstructured environments such as mining, agriculture and urban transport. Modern dense robotic sensor modalities such as CMOS (complementary metal oxide semiconductor) sensors, LIDAR and dense acoustic arrays are best modelled as a fine grid of measu ....Sensing a complex world: Infinite dimensional observer theory for robots. This project aims to develop the foundational theory and design paradigms to support the new generation of sensor systems crucial to enabling widespread robotic automation in unstructured environments such as mining, agriculture and urban transport. Modern dense robotic sensor modalities such as CMOS (complementary metal oxide semiconductor) sensors, LIDAR and dense acoustic arrays are best modelled as a fine grid of measurements from an infinite dimensional dynamical system. The project plans to develop infinite dimensional invariant observer theory to formulate implementable algorithms that run in real-time on embedded hardware, providing detailed information that enables robots to undertake tasks that are presently impossible with state-of-the-art sparse sensing paradigms.Read moreRead less
Geometric observer theory for mechanical control systems. The safety and performance of mechatronic systems such as autonomous drone aircraft and submersibles crucially depends on the algorithms controlling the system. By developing novel observer algorithms that are more stable and more robust this project will contribute to the competitiveness of Australian high-tech companies with mechatronic products.
Exploding solitons. This project builds on previous work in which the existence of exploding solitons was confirmed. Explosions occur regularly in a variety of systems with continuous supply and dissipation of energy. Exploding solitons are more common than ordinary dissipative solitons and occupy large areas in the parameter space. They can be generated relatively easily, however the phenomenon is highly complex. This project aims to further understand exploding solitons so that the phenomeno ....Exploding solitons. This project builds on previous work in which the existence of exploding solitons was confirmed. Explosions occur regularly in a variety of systems with continuous supply and dissipation of energy. Exploding solitons are more common than ordinary dissipative solitons and occupy large areas in the parameter space. They can be generated relatively easily, however the phenomenon is highly complex. This project aims to further understand exploding solitons so that the phenomenon can be used for the generation of pulses with wide spectral output similar to `supercontinuum’ radiation. Research in this direction will provide the basis for building powerful laser sources with wide spectral output.Read moreRead less