Minimizing almost smooth control variation in nonlinear optimal control problems Article Swipe

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Ying Zhang , Changjun Yu , Yingtao Xu , Yanqin Bai ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.3934/jimo.2019023

In this paper, we consider an optimal control problem in which the control is almost smooth and the state and control are subject to terminal state constraints and continuous state and control inequality constraints. By introducing an extra set of differential equations for this almost smooth control, we transform this constrained optimal control problem into an equivalent problem involving both control function and system parameter vector as decision variables. Then, by the control parametrization technique and a time scaling transformation, the equivalent problem is approximated by a sequence of constrained optimal parameter selection problems, each of which is a finite dimensional optimization problem. For each of these constrained optimal parameter selection problems, a novel exact penalty function method is constructed by appending penalized constraint violations to the cost function. This gives rise to a sequence of unconstrained optimal parameter selection problems; and each of which can be solved by existing optimization algorithms or software packages. Finally, a practical container crane operation problem is solved, showing the effectiveness and applicability of the proposed approach.

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Optimal control Mathematical optimization Sequence (biology) Optimization problem Penalty method Mathematics Parametrization (atmospheric modeling) Transformation (genetics) State (computer science) Constraint (computer-aided design) Function (biology) Nonlinear system Computer science Control variable Algorithm Chemistry Gene Physics Radiative transfer Genetics Evolutionary biology Statistics Geometry Quantum mechanics Biology Biochemistry

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Type: article
Language: en
Landing Page: https://doi.org/10.3934/jimo.2019023
PDF: https://www.aimsciences.org/article/exportPdf?id=a888d2b7-316f-4cf2-a613-acda651f2bb4
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Cited By: 6
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DOI: https://doi.org/10.3934/jimo.2019023

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Title: Minimizing almost smooth control variation in nonlinear optimal control problems

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Language: en

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Publication year: 2019

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Publication date: 2019-03-29

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Authors: Ying Zhang, Changjun Yu, Yingtao Xu, Yanqin Bai

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Landing page: https://doi.org/10.3934/jimo.2019023

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Concepts: Optimal control, Mathematical optimization, Sequence (biology), Optimization problem, Penalty method, Mathematics, Parametrization (atmospheric modeling), Transformation (genetics), State (computer science), Constraint (computer-aided design), Function (biology), Nonlinear system, Computer science, Control variable, Algorithm, Chemistry, Gene, Physics, Radiative transfer, Genetics, Evolutionary biology, Statistics, Geometry, Quantum mechanics, Biology, Biochemistry

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Cited by: 6

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Citations by year (recent): 2025: 1, 2022: 1, 2021: 4

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abstract_inverted_index.constraints	26
abstract_inverted_index.constructed	119
abstract_inverted_index.dimensional	100
abstract_inverted_index.introducing	35
abstract_inverted_index.approximated	84
abstract_inverted_index.constraints.	33
abstract_inverted_index.differential	40
abstract_inverted_index.optimization	101, 150
abstract_inverted_index.applicability	168
abstract_inverted_index.effectiveness	166
abstract_inverted_index.unconstrained	136
abstract_inverted_index.parametrization	73
abstract_inverted_index.transformation,	79
cited_by_percentile_year.max	97
cited_by_percentile_year.min	89
countries_distinct_count	0
institutions_distinct_count	4
sustainable_development_goals[0].id	https://metadata.un.org/sdg/16
sustainable_development_goals[0].score	0.6000000238418579
sustainable_development_goals[0].display_name	Peace, Justice and strong institutions
citation_normalized_percentile.value	0.7220798
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False