Obstruction to the billinear control of the Gross-Pitaevskii equation: an example with an unbounded potential

2019/03/11 by Chambrion, Thomas, Thomann, Laurent
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1903.04185

Abstract

In 1982, Ball, Marsden, and Slemrod proved an obstruction to the controllability of linear dynamics with a bounded bilinear control term. This note presents an example of nonlinear dynamics with respect to the state for which this obstruction still holds while the control potential is not bounded.

Related

• On the bilinear control of the Gross-Pitaevskii equation
• On the Ball-Marsden-Slemrod obstruction for bilinear control systems
• A topological obstruction to the controllability of nonlinear wave\n equations with bilinear control term
• Quadratic obstructions to controllability: from ODEs to PDEs
• Bilinear control of evolution equations with unbounded lower order terms. Application to the Fokker-Planck equation