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
Discovery Early Career Researcher Award - Grant ID: DE150100240
Funder
Australian Research Council
Funding Amount
$315,000.00
Summary
Geometry and Conditioning in Structured Conic Problems. Conic programming allows one to model and solve large industrial problems via modern optimisation methods, such as interior-point algorithms. These methods are efficient and reliable in solving a vast number of problems, however, they fail on a relatively small but significant set of ill-posed instances, thus affecting the overall reliability of the technique. The reason for such behaviour is profound and constitutes one of the major unsolv ....Geometry and Conditioning in Structured Conic Problems. Conic programming allows one to model and solve large industrial problems via modern optimisation methods, such as interior-point algorithms. These methods are efficient and reliable in solving a vast number of problems, however, they fail on a relatively small but significant set of ill-posed instances, thus affecting the overall reliability of the technique. The reason for such behaviour is profound and constitutes one of the major unsolved problems in real complexity: there is no known algorithm that solves conic problems with real data in polynomial time. The project aims to develop a deep understanding of the geometry of conic problems, aiming for the resolution of this fundamental problem in computational theory.Read moreRead less
Analysis and design of control systems with saturation and time-delay. Control engineering is an enabling technology without which most modern engineering systems, such as aircrafts or Internet, can not operate properly. Actuator saturation and time-delays are undesirable phenomena that often arise in control systems leading to poor performance and sometimes instability. For example, both of these phenomena arise in control of modern telecommunication systems, such as Active Queue Management in ....Analysis and design of control systems with saturation and time-delay. Control engineering is an enabling technology without which most modern engineering systems, such as aircrafts or Internet, can not operate properly. Actuator saturation and time-delays are undesirable phenomena that often arise in control systems leading to poor performance and sometimes instability. For example, both of these phenomena arise in control of modern telecommunication systems, such as Active Queue Management in TCP networks. The project aims at tackling these phenomena by using recently developed techniques in antiwindup for saturating actuators and by revisiting some classical methods for Smith predictor design for time-delayed systems.Read moreRead less
Large Scale Complex Multiagent Systems : Control Methodologies and Information Architectures. Future military operations are likely to involve increasing use of unmanned vehicles, airborne, underwater or on land. In some cases there will be very large formations. This research will develop methodologies which allow formations of unmanned vehicles to be configured. Much of the same methodology is applicable to the construction and operation of large scale sensor networks, identified by some comm ....Large Scale Complex Multiagent Systems : Control Methodologies and Information Architectures. Future military operations are likely to involve increasing use of unmanned vehicles, airborne, underwater or on land. In some cases there will be very large formations. This research will develop methodologies which allow formations of unmanned vehicles to be configured. Much of the same methodology is applicable to the construction and operation of large scale sensor networks, identified by some commentators as one of the most important technologies of the 21st century. They comprise large numbers of low cost networked sensors and will increasingly find application in security, agricultural and environmental monitoring.Read moreRead less
Innovations in spherical approximation - construction, analysis and applications. The motivating problems for this project come from geophysics, including climate, weather forecasting, planetary gravitation and magnetism, and from coding theory and molecular chemistry. National benefit is expected to arise both from an improved ability to handle problems of key economic importance, and from an enhanced position in the international scientific world, through public presentation in leading journa ....Innovations in spherical approximation - construction, analysis and applications. The motivating problems for this project come from geophysics, including climate, weather forecasting, planetary gravitation and magnetism, and from coding theory and molecular chemistry. National benefit is expected to arise both from an improved ability to handle problems of key economic importance, and from an enhanced position in the international scientific world, through public presentation in leading journals and international conferences, and from direct collaboration with internationally leading scientists from USA, UK and Germany. The project will also increase the pool of trained mathematicians with expertise in areas important for applications.
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Development of robust adaptive and nonlinear control methodologies. Techniques will be developed that will allow industrial plants to operate with lower direct or environmental cost, and airborne vehicles to operate more efficiently or more safely.
Discovery Early Career Researcher Award - Grant ID: DE210101344
Funder
Australian Research Council
Funding Amount
$364,981.00
Summary
Advancing genomic-driven infectious diseases modelling. Emerging infectious diseases and antimicrobial resistance are among the greatest threats to Australian health and agriculture, and current surveillance tools may fail to detect and mitigate infectious disease outbreaks in real time. This project will develop advanced phylodynamic methods (i.e., mathematical models of infectious disease transmission and pathogen evolution) to enable real-time surveillance of infectious disease outbreaks as t ....Advancing genomic-driven infectious diseases modelling. Emerging infectious diseases and antimicrobial resistance are among the greatest threats to Australian health and agriculture, and current surveillance tools may fail to detect and mitigate infectious disease outbreaks in real time. This project will develop advanced phylodynamic methods (i.e., mathematical models of infectious disease transmission and pathogen evolution) to enable real-time surveillance of infectious disease outbreaks as they emerge and monitor levels of drug resistance.Read moreRead less
Safe Adaptive Control. Adaptive controllers are intelligent controllers, which can redesign themselves as they learn more about the environment. There are many algorithms for adaptive controllers; some of them can cause unacceptable behaviour during the learning process. Safe adaptive controllers are those for which this behaviour is ruled out. This project is concerned with developing procedures for guaranteeing the safety property in a wide variety of situations.
Theory and applications of three dimensional fractal transformations. The purpose of this project is to develop the theory and algorithms for a new class of continuous mappings between fractals. Outcomes include a better understanding of fractals, substantially better algorithms for fractal compression and many new applications.
Measurement Feedback Control of Nonlinear and Quantum Systems. The purpose of control systems is to regulate the behaviour of a diverse range of engineering systems including those found in aerospace, manufacturing and telecommunications, as well as in important emerging fields including quantum technology. The aim of this project is to develop measurement feedback design methodologies for systems modelled by nonlinear or quantum dynamics. The project is motivated by the need for systematic meth ....Measurement Feedback Control of Nonlinear and Quantum Systems. The purpose of control systems is to regulate the behaviour of a diverse range of engineering systems including those found in aerospace, manufacturing and telecommunications, as well as in important emerging fields including quantum technology. The aim of this project is to develop measurement feedback design methodologies for systems modelled by nonlinear or quantum dynamics. The project is motivated by the need for systematic methods for robust control system design. A central issue concerns suitable representation and use of measurement information for feedback control.Read moreRead less