A noncommunicative Kalman condition for null controllability of backward stochastic parabolic systems

Mohamed Fadili

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arXiv · 2608.01836

A noncommunicative Kalman condition for null controllability of backward stochastic parabolic systems

Mohamed Fadili

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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.

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Mohamed Fadili. 2026-08-03. A noncommunicative Kalman condition for null controllability of backward stochastic parabolic systems. https://arxiv.org/abs/2608.01836

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