Exact boundary controllability of the Korteweg-de Vries equation

摘要

We consider boundary control of the distributed parameter system described by the Korteweg-de Vries (KdV) equation posed on a finite interval α less than or equal x less than or equal β for t greater than or equal 0. It is shown that by choosing appropriate control inputs one can always guide the system from a given initial state φ to a given terminal state ψ in the time period [0, T] so long as φ and ψ satisfy specified conditions. This exact boundary controllability is established by considering a related initial value control problem of the KdV equation posed on the whole line R. Various recently discovered smoothing properties of the KdV equation have played important roles in our approach.