3 papers
math.OC2026
Data-Driven optimal control via Koopman operators and Hamilton-Jacobi-Bellman equations
Guuyuan Chen, Gaosheng Zhu
This paper presents a data-driven stable manifold (DD-SM) method, which integrates Koopman operator representation learning with the geometric stable manifold approach to Hamilton-…
math.DS2024
The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition
Yuming Xiao, Gaosheng Zhu
In this paper, we prove the existence of periodic solutions with any prescribed minimal period for even second order Hamiltonian systems and convex first order Hamiltonian sy…
math.DS2020
Morse index and Maslov-type index of the discrete Hamiltonian system
Gaosheng Zhu
In this paper, we give the definition of Maslov-type index of the discrete Hamiltonian system, and obtain the relation of Morse index and Maslov-type index of the discrete Hamilton…