Polynomial Turnpike Property for a Class of Infinite-Dimensional Oscillating Systems
Abstract
We establish a polynomial turnpike estimate for an optimal control problem consisting of a system of infinitely many controlled oscillators, considered as an abstract differential equation in a Hilbert space, with a quadratic cost. Our proof relies on spectral considerations and on the construction of a Riesz basis. A concrete example is given, which involves a rotating bodybeam system. To our knowledge, this is the first example of a pointwise turnpike estimate around a steady-state that is polynomial but not exponential.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Spectral Theory in Mathematical Physics
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 2 March 2026
- Language
- EN
- Document type
- Preprint