Optimal Transforms of Random Vectors. This proposal focusses on development of optimal transforms to describe and model nonlinear phenomena when only statistical information is known. An optimal transform is a mathematical procedure that enables us to process information in a way that is most suited to the task in hand. These transforms have been successfully used in approximation, information theory, communications, control theory and signal and image processing. Applications include modelli ....Optimal Transforms of Random Vectors. This proposal focusses on development of optimal transforms to describe and model nonlinear phenomena when only statistical information is known. An optimal transform is a mathematical procedure that enables us to process information in a way that is most suited to the task in hand. These transforms have been successfully used in approximation, information theory, communications, control theory and signal and image processing. Applications include modelling of physical, chemical and biological systems, filtering and compression of signals and data classification and clustering. We propose two new hybrid models for realistic transforms in a general structural framework.
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Duality, singular perturbations and numerical analysis in infinite dimensional linear programming problems related to problems of control of nonlinear dynamical systems. Problems of control of nonlinear dynamical systems attract continued interest of eminent researchers motivated by important applications and by the fact that analytical and/or numerical analysis of a general nonlinear control problem presents a challenging task. The outcomes of the project will be both fundamental theoretical re ....Duality, singular perturbations and numerical analysis in infinite dimensional linear programming problems related to problems of control of nonlinear dynamical systems. Problems of control of nonlinear dynamical systems attract continued interest of eminent researchers motivated by important applications and by the fact that analytical and/or numerical analysis of a general nonlinear control problem presents a challenging task. The outcomes of the project will be both fundamental theoretical results and readily applicable (linear programming based) algorithms that will equip researchers and engineers with new tools for analysis and numerical solution of nonlinear control problems (including problems that have been intractable so far). The project will further enhance Australia's international reputation in Control Theory and its Applications.
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