Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stabilization of higher order Schr\"odinger equations on a finite
  interval: Part II   Backstepping based controller and observer models were designed for higher
order linear and nonlinear Schr\"odinger equations on a finite interval in Part
I of this study where the controller was assumed to be acting from the left
endpoint of the medium. In this companion paper, we further the analysis by
considering boundary controller(s) acting at the right endpoint of the domain.
It turns out that the problem is more challenging in this scenario as the
associated boundary value problem for the backstepping kernel becomes
overdetermined and lacks a smooth solution. The latter is essential to switch
back and forth between the original plant and the so called target system. To
overcome this difficulty we rely on the strategy of using an imperfect kernel,
namely one of the boundary conditions in kernel PDE model is disregarded. The
drawback is that one loses rapid stabilization in comparison with the left
endpoint controllability. Nevertheless, the exponential decay of the $L^2$-norm
with a certain rate still holds. The observer design is associated with new
challenges from the point of view of wellposedness and one has to prove
smoothing properties for an associated initial boundary value problem with
inhomogeneous boundary data. This problem is solved by using Laplace transform
in time. However, the Bromwich integral that inverts the transformed solution
is associated with certain analyticity issues which are treated through a
subtle analysis. Numerical algorithms and simulations verifying the theoretical
results are given.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol