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
Occupational Measures Approach to Long Run Average and Singularly Perturbed Optimal Control Problems. Problems of optimal control of long-run average and singularly perturbed systems arise in many applications. The project will lead to the development of new linear programming based techniques for analyzing these problems (including problems intractable so far) and finding their numerical solutions. The new techniques will have a potential to be further developed into software that can benefit A ....Occupational Measures Approach to Long Run Average and Singularly Perturbed Optimal Control Problems. Problems of optimal control of long-run average and singularly perturbed systems arise in many applications. The project will lead to the development of new linear programming based techniques for analyzing these problems (including problems intractable so far) and finding their numerical solutions. The new techniques will have a potential to be further developed into software that can benefit Australian industries and technologies. The proposed topic is in the focus of interest of many eminent researchers around the world and the dissemination of our results will further improve Australia's standing in the international research community. Read moreRead less