Multiscale deterministic and stochastic singularly perturbed control systems: occupational measures approach
(V Gaitsgory, V Borkar, L Finlay, S Kravchuk, J-B Lasserre, S Rossomakhine and M-T Nguyen, )
A unified averaging technique for analysing deterministic and stochastic
multiscale singularly perturbed control systems is being developed. Such
systems arise as mathematical models of real-world dynamical systems in
which state variables can change their values with rates of different orders
of magnitude.
The technique is based on the assumption that the system, which would describe the dynamics of the fast variables if the slow ones were frozen, exhibits certain ergodicity properties expressed as the existence of its limit occupational measures set. Conditions for the existence of such a set and its structure are also studied.
This project will be funded from the ARC Discovery grant “Multiscale
Singularly Perturbed Control Systems (2003-2005).