Linear partial differential operators or linear delay time systems are effective models for many physical phenomena. Perturbations of these systems can often be modelled by white noise. Typically these models have unknown parameters and the systems must be controlled so there is the problem of stochastic adaptive control for linear, stochastic distributed parameter systems. In many distributed systems there is boundary control. In this proposal some problems of adaptive control for linear, stochastic distributed parameter systems with boundary control are described for investigation. Apparently no results are available on this topic. The problem of stochastic adaptive control for these systems include the exhibition of a consistent family of estimates of the unknown parameters, the continuity of the solution of a Riccati equation with respect to parameters, a generalization of the Ito formula and the verification of the self-optimizing property of a family of adaptive controls. Furthermore the initiation of an investigation of adaptive control for stochastic semilinear parabolic equations is proposed.
