Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic
  Programming   In this paper, we study the sensitivity of discrete-time dynamic programs
with nonlinear dynamics and objective to perturbations in the initial
conditions and reference parameters. Under uniform controllability and
boundedness assumptions for the problem data, we prove that the directional
derivative of the optimal state and control at time $k$, $\boldsymbol{x}^*_{k}$
and $\boldsymbol{u}^*_{k}$, with respect to the reference signal at time $i$,
$\boldsymbol{d}_{i}$, will have exponential decay in terms of $|k-i|$ with a
decay rate $\rho$ independent of the temporal horizon length. The key technical
step is to prove that a version of the convexification approach proposed by
Verschueren et al. can be applied to the KKT conditions and results in a convex
quadratic program with uniformly bounded data. In turn, Riccati techniques can
be further employed to obtain the sensitivity result, borne from the
observation that the directional derivatives are solutions of quadratic
programs with structure similar to the KKT conditions themselves. We validate
our findings with numerical experiments on a small nonlinear, nonconvex,
dynamic program.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph