Quadratic Obstructions to Small-Time Local Controllability for the Multi-Input Bilinear Schrödinger Equation
Abstract
Abstract. We investigate the small-time local controllability (STLC) near the ground state of a bilinear Schrödinger equation when the linearized system is not controllable. It is well known that, for single-input systems, quadratic terms in the state expansion can then lead to obstructions to the STLC of the nonlinear system. In this work, we extend this phenomenon to the multi-input setting, presenting the first example of multi-input quadratic obstructions for PDEs. Our results build upon our previous study of such obstructions for ODEs and provide a functional framework for analyzing them in the bilinear Schrödinger equation.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Numerical methods for differential equations
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- SIAM Journal on Control and Optimization
- Volume
- 64
- Issue
- 3
- Pages
- 2058–2080
- Publication date
- 24 June 2026
- Language
- EN