This article presents a dissipativity approach for robustness analysis using the framework of integral quadratic constraints (IQCs). The derived results apply for linear time‐varying nominal systems with uncertain initial conditions. IQC multipliers are used to describe the sets of allowable uncertainty operators, and signal IQC multipliers are used to describe the sets of allowable disturbance signals. The novel concepts of dichotomic nodes and their corresponding factorizations are introduced, which allow for the aforementioned multipliers to be general time‐varying operators. The results are illustrated via the robustness analysis of a flight controller for an unmanned aircraft system tasked to perform a Split‐S maneuver.
Integral Quadratic Constraints with Infinite-Dimensional Channels
Modern control theory provides us with a spectrum
of methods for studying the interconnection of dynamic
systems using input-output properties of the interconnected subsystems.
Perhaps the most advanced framework for such inputoutput
analysis is the use of Integral Quadratic Constraints
(IQCs), which considers the interconnection of a nominal linear
system with an unmodelled nonlinear or uncertain subsystem
with known input-output properties. Although these methods
are widely used for Ordinary Differential Equations (ODEs),
there have been fewer attempts to extend IQCs to infinitedimensional
systems. In this paper, we present an IQC-based
framework for Partial Differential Equations (PDEs) and Delay
Differential Equations (DDEs). First, we introduce infinitedimensional
signal spaces, operators, and feedback interconnections.
Next, in the main result, we propose a formulation
of hard IQC-based input-output stability conditions, allowing
for infinite-dimensional multipliers. We then show how to test
hard IQC conditions with infinite-dimensional multipliers on a
nominal linear PDE or DDE system via the Partial Integral
Equation (PIE) state-space representation using a sufficient
version of the Kalman-Yakubovich-Popov lemma (KYP). The
results are then illustrated using four example problems with
uncertainty and nonlinearity.
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- PAR ID:
- 10483582
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- Proceedings of the American Control Conference
- ISSN:
- 0743-1619
- ISBN:
- 979-8-3503-2806-6
- Page Range / eLocation ID:
- 1576 to 1583
- Format(s):
- Medium: X
- Location:
- San Diego, CA, USA
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC55779.2023.10156335
