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
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
Stochastic Geometry for Multi-sensor Data Fusion System. The aim of this project is to develop efficient algorithms for tracking and sensor management in a multi-sensor multi-target environment. Finite random set theory provides a natural way of representing a random number of (random) object states, an issue that has been largely ignored in the tracking literature until recently. Although a satisfactory foundation for multiple object filtering has been provided by random set theory, in this ear ....Stochastic Geometry for Multi-sensor Data Fusion System. The aim of this project is to develop efficient algorithms for tracking and sensor management in a multi-sensor multi-target environment. Finite random set theory provides a natural way of representing a random number of (random) object states, an issue that has been largely ignored in the tracking literature until recently. Although a satisfactory foundation for multiple object filtering has been provided by random set theory, in this early stage no algorithm capable of tracking many targets has emerged from this framework. We are confident that efficient algorithms can be developed by exploiting the insights and mathematical tools of stochastic geometryRead moreRead less
HOLOMORPHIC CURVES, REEB FLOWS AND CONTACT TOPOLOGY. Motion of a satellite is one of many examples of a Reeb dynamical system. The aim of the project is to deepen our understanding of Reeb flows. The Reeb flows, in particular, include Hamiltonian flows on three-dimensional contact type energy surfaces. To study the behaviour of Reeb flows we construct systems of global surfaces of section and study the iterates of the Poincare map, which is obtained by following the flow until it hits a surface. ....HOLOMORPHIC CURVES, REEB FLOWS AND CONTACT TOPOLOGY. Motion of a satellite is one of many examples of a Reeb dynamical system. The aim of the project is to deepen our understanding of Reeb flows. The Reeb flows, in particular, include Hamiltonian flows on three-dimensional contact type energy surfaces. To study the behaviour of Reeb flows we construct systems of global surfaces of section and study the iterates of the Poincare map, which is obtained by following the flow until it hits a surface. The main tools in constructing systems of global surfaces of section are holomorphic curves in symplectization, which are defined on punctured Riemann surfaces and solve nonlinear Cauchy-Riemann type operator. These curves are also main ingredients of new invariants of contact and symplectic manifolds.
These new invariants are now known as Contact Homology and Symplectic Field Theory. In the second part of the project we develop analytical foundations for these theories.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
Spectral Theory of Hamiltonian Dynamical Systems. Stability theory of steady states, travelling waves, periodic waves, and other coherent structures in nonlinear Hamiltonian partial differential equations is a cornerstone of modern dynamical systems. In particular it is of utmost importance to reliably compute eigenvalues, which determine the stability or instability of such structures. This project will develop methods to compute the spectrum of Hamiltonian operators in more than one spatial di ....Spectral Theory of Hamiltonian Dynamical Systems. Stability theory of steady states, travelling waves, periodic waves, and other coherent structures in nonlinear Hamiltonian partial differential equations is a cornerstone of modern dynamical systems. In particular it is of utmost importance to reliably compute eigenvalues, which determine the stability or instability of such structures. This project will develop methods to compute the spectrum of Hamiltonian operators in more than one spatial dimension. It will use the powerful geometric tools of the Maslov index and the Evans function. We will use these to simultaneously advance, and bring together the theories of the two dimensional Euler equations and Jacobi operators.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