Exact Controllability for Stochastic First-Order Multi-Dimensional Hyperbolic Systems

Li Z, Lü Q, Wang Y, Yang H (2026)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Article in Edited Volumes

Publication year: 2026

Open Access Link: https://doi.org/10.48550/arXiv.2601.18270

Abstract

This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a boundary control applied to the drift term. By means of a classical duality argument, the controllability problem is reduced to an observability estimate for the corresponding backward stochastic system. The main technical contribution is the establishment of a new global Carleman estimate for such backward systems, combined with a weighted energy identity. This enables us to prove the desired observability inequality under a geometric structural condition (Condition 1.1), which ensures that all characteristic rays propagate toward the boundary within a finite time. As a result, we obtain exact controllability provided the control time T exceeds a sharp threshold T0 given explicitly in terms of the system geometry. Furthermore, we complement the positive result with several negative controllability theorems, which demonstrate that both controls are necessary and must act in a distributed manner. Our analysis not only extends controllability theory from deterministic to stochastic multi-dimensional hyperbolic systems but also provides, as a byproduct, new results for deterministic systems under a structural hypothesis. Applications to stochastic traffic flow, epidemiological models, and shallow-water equations are discussed.

Authors with CRIS profile

Yu Wang Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Haitian Yang Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Sichuan University (SCU) / 四川大学 CN China (CN)

How to cite

APA:

Li, Z., Lü, Q., Wang, Y., & Yang, H. (2026). Exact Controllability for Stochastic First-Order Multi-Dimensional Hyperbolic Systems. (Unpublished, Submitted).

MLA:

Li, Zengyu, et al. Exact Controllability for Stochastic First-Order Multi-Dimensional Hyperbolic Systems. Unpublished, Submitted. 2026.

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