Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Iterative Learning and Extremum Seeking for Repetitive Time-Varying
  Mappings   In this paper, we develop an extremum seeking control method integrated with
iterative learning control to track a time-varying optimizer within finite
time. The behavior of the extremum seeking system is analyzed via an
approximating system - the modified Lie bracket system. The modified Lie
bracket system is essentially an online integral-type iterative learning
control law. The paper contributes to two fields, namely, iterative learning
control and extremum seeking. First, an online integral type iterative learning
control with a forgetting factor is proposed. Its convergence is analyzed via
$k$-dependent (iteration- dependent) contraction mapping in a Banach space
equipped with $\lambda$-norm. Second, the iterative learning extremum seeking
system can be regarded as an iterative learning control with "control input
disturbance." The tracking error of its modified Lie bracket system can be
shown uniformly bounded in terms of iterations by selecting a sufficiently
large frequency. Furthermore, it is shown that the tracking error will finally
converge to a set, which is a $\lambda$-norm ball. Its center is the same with
the limit solution of its corresponding "disturbance-free" system (the
iterative learning control law); and its radius can be controlled by the
frequency.

17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ