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Regular version of the site

Article

On Stochastic Optimality for a Linear Controller with Attenuating Disturbances

Automation and Remote Control. 2013. Vol. 74. No. 4. P. 628-641.
Palamarchuk E. S., Belkina T. A.

For a linear stochastic control system with quadratic objective functional, we introduce
various generalizations of the notions of optimality on average and stochastic optimality
on an infinite time interval that take into account possible degeneration of the parameter of
the disturbing process with time (attenuation of the disturbances) or the presence of a discount
function in the objective functional. This lets us improve upon the quality estimate for a well
known optimal control in this problem from the point of view of both asymptotic behavior of
the functional’s expectation and its asymptotic probabilistic properties. In particular, in the
considered case we have found an improvement for the well known logarithmic upper bound on
the optimal control for a family of defect processes.