A noncommunicative Kalman condition for null controllability of backward stochastic parabolic systems
Year: 2026
Type: preprint
Abstract: We study null controllability of backward stochastic heat systems with constant couplings in both the state and the martingale integrand, common scalar diffusion, and a localized drift control. We prove that null controllability is equivalent to a noncommutative word-rank condition on the two coupling matrices and the control matrix. The proof combines a factorization of the dual dynamics, positivity and small-time coercivity of a finite-dimensional stochastic Gramian, and a Lebeau--Robbiano spectral argument. Failure of the rank condition yields an invariant unobservable subspace.
Source: arXiv (Cornell University)
Author: Fadili, Mohamed
Institutions: Cadi Ayyad University, École Normale Supérieure - Marrakech
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7172435890