Dynamic Analysis and Control for Hybrid Systems and Networks. Hybrid systems are now accepted as the best way to model many high-tech situations in transport, energy management, networking, household and industrial automation. This project will develop the theoretical tools needed to ensure such systems operate stably and efficiently despite imperfections and outside disturbances.
What predictions can I trust? Stability of chaotic random dynamical systems. This project aims to make significant progress on the intricate question of global stability of non-autonomous chaotic dynamical systems. Using ergodic theory, this project expects to determine when and how errors in dynamical models that are small and frequent, or large and infrequent, can cause dramatic changes in meaningful mathematical model outputs. Expected outcomes include the discovery of mathematical mechanisms ....What predictions can I trust? Stability of chaotic random dynamical systems. This project aims to make significant progress on the intricate question of global stability of non-autonomous chaotic dynamical systems. Using ergodic theory, this project expects to determine when and how errors in dynamical models that are small and frequent, or large and infrequent, can cause dramatic changes in meaningful mathematical model outputs. Expected outcomes include the discovery of mathematical mechanisms underlying large-scale (in)stability for time-dependent dynamical systems, and reliable numerical methods for detecting instabilities. This research is expected to lead to improved characterisations of shocks or collapse in externally driven dynamical systems and assist scientists to gauge which predictions they can trust.Read moreRead less
Modern mathematics to unravel the birth of coherence in dynamical systems. This project aims to reveal the precise mathematical mechanisms underlying the emergence and disappearance of long-lived coherent features in dynamical systems. This project expects to generate new fundamental mathematics in the area of dynamical systems, using innovative operator-theoretic approaches to carefully tease apart the lifecycles of coherent structures. The expected outcomes of this project include new mathemat ....Modern mathematics to unravel the birth of coherence in dynamical systems. This project aims to reveal the precise mathematical mechanisms underlying the emergence and disappearance of long-lived coherent features in dynamical systems. This project expects to generate new fundamental mathematics in the area of dynamical systems, using innovative operator-theoretic approaches to carefully tease apart the lifecycles of coherent structures. The expected outcomes of this project include new mathematical theory and computational algorithms to anticipate the genesis and destruction of coherent objects, which are key organisers of complex geophysical flows. This breakthrough mathematics should provide significant benefits, such as improved prediction of eddy transport and persistence of weather and climate patterns.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE160100147
Funder
Australian Research Council
Funding Amount
$381,294.00
Summary
Coherent structures in chaotic dynamical systems. Using transfer operators and state-of-the-art multiplicative ergodic theory as a springboard, this project aims to develop innovative mathematics for bridging gaps between dynamical systems theory and applications. Coherent structures, such as oceanic eddies and atmospheric vortices, are prevalent in real-world dynamical systems and play a crucial role in both weather and climate systems. These structures arise in externally forced systems, and t ....Coherent structures in chaotic dynamical systems. Using transfer operators and state-of-the-art multiplicative ergodic theory as a springboard, this project aims to develop innovative mathematics for bridging gaps between dynamical systems theory and applications. Coherent structures, such as oceanic eddies and atmospheric vortices, are prevalent in real-world dynamical systems and play a crucial role in both weather and climate systems. These structures arise in externally forced systems, and the existing theory concerning their location, number and stability to model errors is much less understood than in the non-forced counterpart. The intended outcomes include new algorithms for the automatic detection of coherent structures and results about their stability under perturbations which are relevant to roles in both weather and climate systems.Read moreRead less
New mathematics to quantify fluctuations and extremes in dynamical systems. Many problems in the natural world result from the cumulative effect of extreme events in complex dynamical systems. Dynamical models of ecological and physical processes have internal variables that can combine to produce large observable changes. Quantitative estimation of the variability of these chaotic models is difficult because of the time dependence of the dynamics and their “long memory” due to significant deter ....New mathematics to quantify fluctuations and extremes in dynamical systems. Many problems in the natural world result from the cumulative effect of extreme events in complex dynamical systems. Dynamical models of ecological and physical processes have internal variables that can combine to produce large observable changes. Quantitative estimation of the variability of these chaotic models is difficult because of the time dependence of the dynamics and their “long memory” due to significant deterministic components. This project aims to develop mathematics and numerics to accurately quantify and assess these complicated variations. The project expects to provide powerful tools to predict harmful outcomes in biogeophysical systems, and assist with the development of mitigation strategies.Read moreRead less
Coordination control of underactuated ocean vehicles for ocean forecasting. Australia is surrounded by oceans. Ocean forecasting is essential for effective and efficient operations on and within the ocean for a number of applications such as coastal zone management, military operations and scientific research. The successful completion of this project promises to put Australia in a leading position in this area. Due to the multi-disciplinary nature of this project, the project development will a ....Coordination control of underactuated ocean vehicles for ocean forecasting. Australia is surrounded by oceans. Ocean forecasting is essential for effective and efficient operations on and within the ocean for a number of applications such as coastal zone management, military operations and scientific research. The successful completion of this project promises to put Australia in a leading position in this area. Due to the multi-disciplinary nature of this project, the project development will also stimulate the development in many other areas such as new ocean vehicles, sensors and actuators, electronics and control.Read moreRead less
Emergence of modular structure in complex systems. Complex systems pervade our world, but are still poorly understood. Self-contained modules provide the most widespread and effective way of reducing and managing complexity, but the way they form in natural systems remains largely a mystery. This study investigates mechanisms that contribute to module formation in complex networks, including adaptation, clustering, enslavement, feedback, phase change and synchronisation. Outcomes will include in ....Emergence of modular structure in complex systems. Complex systems pervade our world, but are still poorly understood. Self-contained modules provide the most widespread and effective way of reducing and managing complexity, but the way they form in natural systems remains largely a mystery. This study investigates mechanisms that contribute to module formation in complex networks, including adaptation, clustering, enslavement, feedback, phase change and synchronisation. Outcomes will include insights into the organisation and functioning of many complex systems, including the Internet, ecological communities and genetic networks. Practical outcomes will include new modelling tools and applications both to evolutionary computation and the design and control of large information networks.Read moreRead less
Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can ....Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can help Australian energy industry to reduce greenhouse emissions. It will also result in education of the next generation research leaders in this emerging field.Read moreRead less
DEVELOPMENT OF NEW NONLINEAR CONTROLLERS FOR TRAJECTORY TRACKING AND PATH-FOLLOWING OF UNDERACTUATED OCEAN VEHICLES. Trajectory tracking control and path-following of underactuated ocean vehicles are not only of theoretical challenging but also important practice. This project is firstly to develop methodologies to design full-state feedback controllers to force the underactuated ocean vehicles including surface ships and underwater vehicles with off-diagonal terms in their system matrices to tr ....DEVELOPMENT OF NEW NONLINEAR CONTROLLERS FOR TRAJECTORY TRACKING AND PATH-FOLLOWING OF UNDERACTUATED OCEAN VEHICLES. Trajectory tracking control and path-following of underactuated ocean vehicles are not only of theoretical challenging but also important practice. This project is firstly to develop methodologies to design full-state feedback controllers to force the underactuated ocean vehicles including surface ships and underwater vehicles with off-diagonal terms in their system matrices to track reference trajectories generated by virtual vehicles, and to follow a predefined path with a desired forward speed. Secondly, we develop methods to design observers to estimate the unmeasured states (velocities) of the vehicles and incorporate with the full-state feedback controllers to have output-feedback observer-based controllers. Lastly, the proposed control design methods are extended to a certain class of underactuated mechanical systems.Read moreRead less
A novel framework for designing input excitation for system identification. Engineers need mathematical models describing the behaviour of the components they use in their design. This project aims at resolving some critical issues faced by the researchers developing cutting edge mathematical software for building such models.