A Convex Optimization Approach to Compute Trapping Regions for Lossless Quadratic Systems Article Swipe

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Shih‐Chi Liao , A. Leonid Heide , Maziar S. Hemati , Peter Seiler ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2401.04787

Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a bounded set. Conditions for the existence and characterization of trapping regions have been established in prior works for boundedness analysis. However, prior solutions have used non-convex optimization methods, resulting in conservative estimates. In this paper, we build on this prior work and provide a convex semidefinite programming condition for the existence of a trapping region. The condition allows precise verification or falsification of the existence of a trapping region. If a trapping region exists, then we provide a second semidefinite program to compute the least conservative trapping region in the form of a ball. Two low-dimensional systems are provided as examples to illustrate the results. A third high-dimensional example is also included to demonstrate that the computation required for the analysis can be scaled to systems of up to $\sim O(100)$ states. The proposed method provides a precise and computationally efficient numerical approach for computing trapping regions. We anticipate this work will benefit future studies on modeling and control of lossless quadratic dynamical systems.

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Semidefinite programming Quadratic equation Lossless compression Regular polygon Bounded function Computation Trapping Quadratic programming Quadratically constrained quadratic program Mathematical optimization Convex optimization Lossy compression Computer science Applied mathematics Mathematics Algorithm Mathematical analysis Geometry Data compression Artificial intelligence Biology Ecology

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2401.04787
PDF: https://arxiv.org/pdf/2401.04787
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Related Works: 10
OpenAlex ID: https://openalex.org/W4390810148

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DOI: https://doi.org/10.48550/arxiv.2401.04787

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Title: A Convex Optimization Approach to Compute Trapping Regions for Lossless Quadratic Systems

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Language: en

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Publication year: 2024

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Publication date: 2024-01-09

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Authors: Shih‐Chi Liao, A. Leonid Heide, Maziar S. Hemati, Peter Seiler

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Landing page: https://arxiv.org/abs/2401.04787

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Concepts: Semidefinite programming, Quadratic equation, Lossless compression, Regular polygon, Bounded function, Computation, Trapping, Quadratic programming, Quadratically constrained quadratic program, Mathematical optimization, Convex optimization, Lossy compression, Computer science, Applied mathematics, Mathematics, Algorithm, Mathematical analysis, Geometry, Data compression, Artificial intelligence, Biology, Ecology

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abstract_inverted_index.efficient	174
abstract_inverted_index.existence	39, 84, 98
abstract_inverted_index.including	10
abstract_inverted_index.numerical	175
abstract_inverted_index.quadratic	4, 195
abstract_inverted_index.resulting	62
abstract_inverted_index.solutions	56
abstract_inverted_index.Conditions	36
abstract_inverted_index.anticipate	182
abstract_inverted_index.atmosphere	13
abstract_inverted_index.estimates.	65
abstract_inverted_index.eventually	27
abstract_inverted_index.illustrate	136
abstract_inverted_index.non-convex	59
abstract_inverted_index.boundedness	52
abstract_inverted_index.computation	150
abstract_inverted_index.demonstrate	147
abstract_inverted_index.established	47
abstract_inverted_index.programming	80
abstract_inverted_index.conservative	64, 119
abstract_inverted_index.optimization	60
abstract_inverted_index.semidefinite	79, 113
abstract_inverted_index.trajectories	26
abstract_inverted_index.verification	93
abstract_inverted_index.applications,	9
abstract_inverted_index.falsification	95
abstract_inverted_index.incompressible	15
abstract_inverted_index.computationally	173
abstract_inverted_index.low-dimensional	129
abstract_inverted_index.characterization	41
abstract_inverted_index.high-dimensional	141
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	4
sustainable_development_goals[0].id	https://metadata.un.org/sdg/13
sustainable_development_goals[0].score	0.41999998688697815
sustainable_development_goals[0].display_name	Climate action
citation_normalized_percentile