Ergodic boundary and point control for linear stochastic PDEs driven by a cylindrical Lévy process

Abstract

An ergodic control problem is studied for controlled linear stochastic equations driven by cylindrical Levy noise with unbounded control operator in a Hilbert space. A family of optimal controls is shown to consist of those asymptotically achieving the feedback form that employs the corresponding Riccati equation. The formula for optimal cost is given. The general results are applied to stochastic heat equation with boundary control and to stochastic structurally damped plate equations with point control.