SEMINARIESCHEMA FÖR MATEMATISK STATISTIK 

Fredag    16/8  15.15         Michael Taksar
          1996                Department of Applied Mathematics,
                              SUNY Stony Brook, New York


                              SINGULAR CONTROL OF MULTIDIMENSIONAL
                              STOCHASTIC PROCESSES
                              

Abstract:

We consider a dynamical system subject to random disturbances modelled by
a diffusion processes. We have to keep the system close to the prescribed
position, however any changes imposed by a controller involve certain costs.
There are also costs related to the distance of the system from the
required position . The objective is to minimize the total expected cost.

This problem is motivated by studying the optimal control of the dissipative
system under uncertainty. The latter can represent a mechanical system subject
to random perturbations, such a cruise control of an aircraft under uncertain
wind conditions, or an electrical system with noise modelled by a diffusion
process (e.g., white noise).

We consider the model in which there are no restriction on the drift (which is
under our control), moreover the drift can take on infinite values. These
models are often appear in the context of constraints being very large or
in the case when the control is of a nonphysical nature.

The optimal policy in these models turns out to be of a different qualitative
nature compared to the classical situation. It consists of keeping the
controlled process in an a priori unknown boundary with minimal effort.
The optimal boundaries can be found from a solution to a second
order partial differential equation with gradient constraints (the
so-called variational inequality). The optimal control is the functional
which maintain oblique reflection of the controlled process from this
boundary. We will also give a natural interpretation of this type of control.





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