  In this paper, a novel control strategy namely disturbance observer-based
control is first applied to stabilization and disturbance rejection for an
anti-stable stochastic heat equation with Neumann boundary actuation and
unknown boundary external disturbance generated by an exogenous system. A
disturbance observer-based boundary control is designed based on the
backstepping approach and estimation/cancellation strategy, where the unknown
disturbance is estimated in real time by a disturbance observer and rejected in
the closed-loop, while the in-domain multiplicative noise whose intensity is
within a known finite interval is attenuated. It is shown that the resulting
closed-loop system is exponentially stable in the sense of both mean square and
almost surely. A numerical example is demonstrated to validate the
effectiveness of the proposed control approach.

Optimization and Control