Construction of optimal observation processes (Q1910979)

Following Kurzhanski (1977), the author analyzes a problem of optimal observation planning. It is supposed that the observation \(y\) depends on an estimated parameter vector \(\theta\) by the linear relation \[ y(t)= a^*(t) \theta+ \xi(t), \] where \(\xi(t)\) is a disturbance having bounded energy. The coefficients \(a(t)\) are supposed to be controlled but non-directly: \[ \dot a= Aa+ Bu, \] where \(u\) is the ``true'' control. The optimality criteria are the determinant or the trace of the matrix \(P^{- 1}\), where \[ P= \int^T_0 aa^* dt \] determines the size of the error ellipsoid. Pontryagin type general conditions of optimality are presented but the main attention is paid to the simplest case \(A= 0\), \(B= 0\), for which explicit results are presented.