A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for e ....A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for efficient use. Superfractals and the associated colouring algorithm could be used to develop a new system to produce synthetic content for wireless devices that would require only low bandwidth.Read moreRead less
Aggregating Generalised Stochastic Petri Nets for improved Performance Analysis. Australia's economy is very dependent on the operation of complex man-made systems. Important examples are telecommunication networks and services (e.g. the Internet), manufacturing plants, organisational processes, military logistics and transport systems (e.g. air traffic control). The performance of these systems is critical to their success. Thus being able to predict performance before systems are implemented i ....Aggregating Generalised Stochastic Petri Nets for improved Performance Analysis. Australia's economy is very dependent on the operation of complex man-made systems. Important examples are telecommunication networks and services (e.g. the Internet), manufacturing plants, organisational processes, military logistics and transport systems (e.g. air traffic control). The performance of these systems is critical to their success. Thus being able to predict performance before systems are implemented is very important in their design. This project will develop leading-edge performance analysis techniques and tools for an important class of practical systems. There is potential to commercialise the resulting tools and methodology and to transfer the expertise to industry.Read moreRead less
Advanced Sweep-Line State Space Reduction Methods for Verification of Concurrent and Distributed Systems. The rigorous design and analysis of distributed systems, such as the Internet and its applications, is known to be a difficult problem. This project will develop new techniques for reducing the memory and time required for computer-aided verification of concurrent and distributed systems. The technique will be combined with other reduction techniques to increase their range of applicability. ....Advanced Sweep-Line State Space Reduction Methods for Verification of Concurrent and Distributed Systems. The rigorous design and analysis of distributed systems, such as the Internet and its applications, is known to be a difficult problem. This project will develop new techniques for reducing the memory and time required for computer-aided verification of concurrent and distributed systems. The technique will be combined with other reduction techniques to increase their range of applicability. The reduction techniques will be implemented and evaluated using important transaction protocols for electronic commerce and internet enabled wireless communications. The technique will also be applied to so called 'object-oriented' modelling languages.Read moreRead less
A Study of Stabilisation and Optimal Control Computation of Impulsive Control Systems. Impulsive systems exhibit the phenomenon of jumps occurring at various time points along their trajectories. They arise from many applications, such as determining appropriate levels of drug administration in cancer and diabetes treatment, optimizing investment strategies in capacity expansion, and sustainable optimal forest management. This project will result in fundamental theory on stability and efficient ....A Study of Stabilisation and Optimal Control Computation of Impulsive Control Systems. Impulsive systems exhibit the phenomenon of jumps occurring at various time points along their trajectories. They arise from many applications, such as determining appropriate levels of drug administration in cancer and diabetes treatment, optimizing investment strategies in capacity expansion, and sustainable optimal forest management. This project will result in fundamental theory on stability and efficient computational algorithms and software packages for stabilizing controls and optimal controls of impulsive control problems. The outcomes will enhance Australia's reputation for leading edge research and facilitate opportunity for international collaboration. It will also provide an excellent opportunity for research training.Read moreRead less
Multiscale Singularly Perturbed Control Systems. We propose to develop a unified averaging technique to analyse deterministic and stochastic multiscale singularly perturbed control systems. Such systems arise as mathematical models of real-world dynamical systems in which state variables can change their values with the rates of different orders of magnitude. The technique is based on the assumption that the system, which would describe the dynamics of the fast state variables if slow ones were ....Multiscale Singularly Perturbed Control Systems. We propose to develop a unified averaging technique to analyse deterministic and stochastic multiscale singularly perturbed control systems. Such systems arise as mathematical models of real-world dynamical systems in which state variables can change their values with the rates of different orders of magnitude. The technique is based on the assumption that the system, which would describe the dynamics of the fast state variables if slow ones were frozen, possesses certain ergodicity properties expressed in the existence of its limit occupational measures set. Conditions for the existence of such a set will be studied and its structure will be described.Read moreRead less
Development of Identification Methods for Nonlinear Dynamical Systems. It is widely recognized that nonlinear systems theory will mark a new era of control science in the coming decade, and will be used in various types of applications. Driven by such immense opportunities and needs, identification of nonlinear systems is emerging as a vital, active area of research. The success of this project will enhance Australia's leading role in the international control community. The training of the post ....Development of Identification Methods for Nonlinear Dynamical Systems. It is widely recognized that nonlinear systems theory will mark a new era of control science in the coming decade, and will be used in various types of applications. Driven by such immense opportunities and needs, identification of nonlinear systems is emerging as a vital, active area of research. The success of this project will enhance Australia's leading role in the international control community. The training of the postdoctoral research associates will generate the expertise needed to maintain the involvement of the coming generation in cutting-edge technological advancement. The project will strengthen research activities in Australia through strong international collaborations.Read moreRead less
An Investigation into Performance Limitation of Wireless Networked Feedback Systems. Recent technological advances in information technology have begun to drive controls research in a direction that seeks to merge communication networks, control design, and computing power. Investigation of the constraints, limitations, and tradeoffs in design of wireless networked control systems is of intrinsic scientific interest and broad engineering impact. The success of this project will enrich Australia' ....An Investigation into Performance Limitation of Wireless Networked Feedback Systems. Recent technological advances in information technology have begun to drive controls research in a direction that seeks to merge communication networks, control design, and computing power. Investigation of the constraints, limitations, and tradeoffs in design of wireless networked control systems is of intrinsic scientific interest and broad engineering impact. The success of this project will enrich Australia's leading role in the international control community. The training of the postdoctoral research associates will generate the expertise needed to maintain the coming generation involved in cutting-edge technological advancement. The project will strengthen research activities in Australia through strong international collaborations.Read moreRead less
Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications. We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analy ....Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications. We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analysis and asymptotic optimisation of singularly perturbed control systems and Markov decision processes. In particular, we plan to establish links between general nonlinear optimal control problems with time average criteria and linear programming problems in the space of limit occupational measures generated by the underlying control system.Read moreRead less
Building correct-by-construction distributed systems from specifications stating how agents' knowledge evolves over time. Many distributed computer system implementations fail to comply with their original informal requirement specification. These requirements typically refer to the migration of information through the system over time, but current specification languages are not rich enough to express such requirements on a sufficiently abstract level. This results in a huge error-provoking gap ....Building correct-by-construction distributed systems from specifications stating how agents' knowledge evolves over time. Many distributed computer system implementations fail to comply with their original informal requirement specification. These requirements typically refer to the migration of information through the system over time, but current specification languages are not rich enough to express such requirements on a sufficiently abstract level. This results in a huge error-provoking gap between the informal requirements and the starting point of formally verifiable development. To minimise this gap, we develop a particularly expressive specification language, a calculus for stepwise refinement from such specifications down to distributed systems, and an automated tool for checking and supporting refinement steps in the calculus.Read moreRead less
A framework for optimisation and concurrent design in photonics. This project will develop a concurrent engineering framework for the design and optimisation of photonic devices, specifically microstructured fibres and Bragg gratings. Novel fibre designs and pulse manipulation grating designs for the telecommunications, automotive and sensing sectors will be developed. New algorithms for the analysis of perturbations and imperfections arising from manufacturing processes will be incorporated int ....A framework for optimisation and concurrent design in photonics. This project will develop a concurrent engineering framework for the design and optimisation of photonic devices, specifically microstructured fibres and Bragg gratings. Novel fibre designs and pulse manipulation grating designs for the telecommunications, automotive and sensing sectors will be developed. New algorithms for the analysis of perturbations and imperfections arising from manufacturing processes will be incorporated into an integrated optimisation framework that uses evolutionary algorithms. Neural networks will be trained to learn the underlying relationships between structural design parameters and device performance parameters. The new concurrent engineering framework will also identify the critical points in fabrication technologies impeding further progress.Read moreRead less