Region of Attraction Estimation Using Union Theorem in Sum-of-Squares Optimization Article Swipe

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Bhaskar Biswas , Dmitry Ignatyev , Argyrios Zolotas , Antonios Tsourdos ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2305.11655

Appropriate estimation of Region of Attraction for a nonlinear dynamical system plays a key role in system analysis and control design. Sum-of-Squares optimization is a powerful tool enabling Region of Attraction estimation for polynomial dynamical systems. Employment of a positive definite function called shape function within the Sum-of-Squares procedure helps to find a richer representation of the Lyapunov function and a larger corresponding Region of Attraction estimation. However, existing Sum-of-Squares optimization techniques demonstrate very conservative results. The main novelty of this paper is the Union theorem which enables the use of multiple shape functions to create a polynomial Lyapunov function encompassing all the areas generated by the shape functions. The main contribution of this paper is a novel computationally-efficient numerical method for Region of Attraction estimation, which remarkably improves estimation performance and overcomes limitations of existing methods, while maintaining the resultant Lyapunov function polynomial, thus facilitating control system design and construction of control Lyapunov function with enhanced Region of Attraction using conventional Sum-of-Squares tools. A mathematical proof of the Union theorem along with its application to the numerical algorithm of Region of Attraction estimation is provided. The method yields significantly enlarged Region of Attraction estimations even for systems with non-symmetric or unbounded Region of Attraction, which is demonstrated via simulations of several benchmark examples.

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Fatal Attraction (2023 Tv Series)

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Mathematical Analysis

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Attraction Lyapunov function Polynomial Mathematics Explained sum of squares Function (biology) Lyapunov exponent Least-squares function approximation Control-Lyapunov function Benchmark (surveying) Representation (politics) Mathematical optimization Lyapunov redesign Applied mathematics Nonlinear system Mathematical analysis Law Statistics Philosophy Political science Geography Physics Linguistics Geodesy Politics Quantum mechanics Biology Evolutionary biology Estimator

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2305.11655
PDF: https://arxiv.org/pdf/2305.11655
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Cited By: 1
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DOI: https://doi.org/10.48550/arxiv.2305.11655

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Title: Region of Attraction Estimation Using Union Theorem in Sum-of-Squares Optimization

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Language: en

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Publication year: 2023

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Publication date: 2023-05-19

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Authors: Bhaskar Biswas, Dmitry Ignatyev, Argyrios Zolotas, Antonios Tsourdos

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Landing page: https://arxiv.org/abs/2305.11655

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Concepts: Attraction, Lyapunov function, Polynomial, Mathematics, Explained sum of squares, Function (biology), Lyapunov exponent, Least-squares function approximation, Control-Lyapunov function, Benchmark (surveying), Representation (politics), Mathematical optimization, Lyapunov redesign, Applied mathematics, Nonlinear system, Mathematical analysis, Law, Statistics, Philosophy, Political science, Geography, Physics, Linguistics, Geodesy, Politics, Quantum mechanics, Biology, Evolutionary biology, Estimator

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abstract_inverted_index.larger	61
abstract_inverted_index.method	120, 187
abstract_inverted_index.richer	53
abstract_inverted_index.system	10, 16, 147
abstract_inverted_index.tools.	163
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abstract_inverted_index.yields	188
abstract_inverted_index.control	19, 146, 152
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abstract_inverted_index.enables	87
abstract_inverted_index.novelty	78
abstract_inverted_index.several	211
abstract_inverted_index.systems	197
abstract_inverted_index.theorem	85, 170
abstract_inverted_index.However,	67
abstract_inverted_index.Lyapunov	57, 98, 141, 153
abstract_inverted_index.analysis	17
abstract_inverted_index.definite	40
abstract_inverted_index.enabling	27
abstract_inverted_index.enhanced	156
abstract_inverted_index.enlarged	190
abstract_inverted_index.existing	68, 135
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abstract_inverted_index.improves	128
abstract_inverted_index.methods,	136
abstract_inverted_index.multiple	91
abstract_inverted_index.positive	39
abstract_inverted_index.powerful	25
abstract_inverted_index.results.	75
abstract_inverted_index.systems.	35
abstract_inverted_index.algorithm	178
abstract_inverted_index.benchmark	212
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abstract_inverted_index.examples.	213
abstract_inverted_index.functions	93
abstract_inverted_index.generated	104
abstract_inverted_index.nonlinear	8
abstract_inverted_index.numerical	119, 177
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abstract_inverted_index.procedure	48
abstract_inverted_index.provided.	185
abstract_inverted_index.resultant	140
abstract_inverted_index.unbounded	201
abstract_inverted_index.Attraction	5, 30, 65, 124, 159, 182, 193
abstract_inverted_index.Employment	36
abstract_inverted_index.estimation	1, 31, 129, 183
abstract_inverted_index.functions.	108
abstract_inverted_index.polynomial	33, 97
abstract_inverted_index.remarkably	127
abstract_inverted_index.techniques	71
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abstract_inverted_index.Attraction,	204
abstract_inverted_index.application	174
abstract_inverted_index.demonstrate	72
abstract_inverted_index.estimation,	125
abstract_inverted_index.estimation.	66
abstract_inverted_index.estimations	194
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abstract_inverted_index.simulations	209
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abstract_inverted_index.construction	150
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abstract_inverted_index.conventional	161
abstract_inverted_index.demonstrated	207
abstract_inverted_index.encompassing	100
abstract_inverted_index.facilitating	145
abstract_inverted_index.mathematical	165
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abstract_inverted_index.corresponding	62
abstract_inverted_index.non-symmetric	199
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abstract_inverted_index.representation	54
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cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	4
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citation_normalized_percentile