Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality and $H_{\infty}$-Optimal Control Of Coupled ODE-PDE Systems   In this paper, we present a convex formulation of $H_{\infty}$-optimal
control problem for coupled linear ODE-PDE systems with one spatial dimension.
First, we reformulate the coupled ODE-PDE system as a Partial Integral Equation
(PIE) system and show that stability and $H_{\infty}$ performance of the PIE
system implies that of the ODE-PDE system. We then construct a dual PIE system
and show that asymptotic stability and $H_{\infty}$ performance of the dual
system is equivalent to that of the primal PIE system. Next, we pose a convex
dual formulation of the stability and $H_{\infty}$-performance problems using
the Linear PI Inequality (LPI) framework. LPIs are a generalization of LMIs to
Partial Integral (PI) operators and can be solved using PIETOOLS, a MATLAB
toolbox. Next, we use our duality results to formulate the stabilization and
$H_{\infty}$-optimal state-feedback control problems as LPIs. Finally, we
illustrate the accuracy and scalability of the algorithms by constructing
controllers for several numerical examples.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph