Ikeda and Sakamoto studied a dynamical control problem called the linear first integral for holonomic dynamical systems, and our proposition proved the same result as theirs in integrability. Also, a symplectic Haantjes manifolds has been defined by Tempesta and Tondo, which is a characterization of integrable systems using $(1,1)$ tensor fields. We show integrability in dynamical control problems from a geometric point of view by means of a concrete construction of a symplectic Haantjes manifold.
"Integrability Theorems of Free Systems and Symplectic Haantjes Structures." J. Geom. Symmetry Phys. 63 39 - 64, 2022. https://doi.org/10.7546/jgsp-63-2022-39-64