Locally optimal failure-protective control (Q1386993)

This paper solves a problem of optimal failure-protective control with respect to a local criterion. Assume that the behavior of the control object is described by a vector stochastic equation and failure causes the change of coordinates of the object, where the failure rate depends on the current change of coordinates. Then a control law is derived for the loss function, which is given by the sum of a function of current losses, a function of losses in time from the beginning of control to the current time instant and a function of losses depending on the failure rate. The derivation is straightforward by using the results of Kazakov. \{Equation (1.1) should read as \(\dot {\mathbf y}={\mathbf a}({\mathbf y})+{\mathbf b}({\mathbf y},{\mathbf u})+\Gamma {\mathbf \xi}\), \({\mathbf y}(0)={\mathbf y}\}\).