Convergence of Iterative Quadratic Programming for Robust Fixed-Endpoint Transfer of Bilinear Systems Article Swipe
Luke S. Baker
,
André Luiz P. de Lima
,
Anatoly Zlotnik
,
Jr-Shin Li
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2403.18131
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2403.18131
We present a computational method for open-loop minimum-norm control synthesis for fixed-endpoint transfer of bilinear ensemble systems that are indexed by two continuously varying parameters. We suppose that one ensemble parameter scales the homogeneous, linear part of the dynamics, and the second parameter scales the effect of the applied control inputs on the inhomogeneous, bilinear dynamics. This class of dynamical systems is motivated by robust quantum control pulse synthesis, where the ensemble parameters correspond to uncertainty in the free Hamiltonian and inhomogeneity in the control Hamiltonian, respectively. Our computational method is based on polynomial approximation of the ensemble state in parameter space and discretization of the evolution equations in the time domain using a product of matrix exponentials corresponding to zero-order hold controls over the time intervals. The dynamics are successively linearized about control and trajectory iterates to formulate a sequence of quadratic programs for computing perturbations to the control that successively improve the objective until the iteration converges. We use a two-stage computation to first ensure transfer to the desired terminal state, and then minimize the norm of the control function. The method is demonstrated for the canonical uniform transfer problem for the Bloch system that appears in nuclear magnetic resonance, as well as the matter-wave splitting problem for the Raman-Nath system that appears in ultra-cold atom interferometry.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2403.18131
- https://arxiv.org/pdf/2403.18131
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4393299969
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https://openalex.org/W4393299969Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2403.18131Digital Object Identifier
- Title
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Convergence of Iterative Quadratic Programming for Robust Fixed-Endpoint Transfer of Bilinear SystemsWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
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2024-03-26Full publication date if available
- Authors
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Luke S. Baker, André Luiz P. de Lima, Anatoly Zlotnik, Jr-Shin LiList of authors in order
- Landing page
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https://arxiv.org/abs/2403.18131Publisher landing page
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https://arxiv.org/pdf/2403.18131Direct link to full text PDF
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2403.18131Direct OA link when available
- Concepts
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Convergence (economics), Bilinear interpolation, Quadratic equation, Fixed point, Mathematics, Mathematical optimization, Quadratic programming, Sequential quadratic programming, Applied mathematics, Computer science, Mathematical analysis, Economics, Statistics, Economic growth, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
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1Total citation count in OpenAlex
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| abstract_inverted_index.correspond | 73 |
| abstract_inverted_index.intervals. | 126 |
| abstract_inverted_index.linearized | 131 |
| abstract_inverted_index.parameters | 72 |
| abstract_inverted_index.polynomial | 93 |
| abstract_inverted_index.resonance, | 201 |
| abstract_inverted_index.synthesis, | 68 |
| abstract_inverted_index.trajectory | 135 |
| abstract_inverted_index.ultra-cold | 216 |
| abstract_inverted_index.zero-order | 120 |
| abstract_inverted_index.Hamiltonian | 79 |
| abstract_inverted_index.computation | 163 |
| abstract_inverted_index.matter-wave | 206 |
| abstract_inverted_index.parameters. | 24 |
| abstract_inverted_index.uncertainty | 75 |
| abstract_inverted_index.Hamiltonian, | 85 |
| abstract_inverted_index.continuously | 22 |
| abstract_inverted_index.demonstrated | 185 |
| abstract_inverted_index.exponentials | 117 |
| abstract_inverted_index.homogeneous, | 33 |
| abstract_inverted_index.minimum-norm | 7 |
| abstract_inverted_index.successively | 130, 151 |
| abstract_inverted_index.approximation | 94 |
| abstract_inverted_index.computational | 3, 88 |
| abstract_inverted_index.corresponding | 118 |
| abstract_inverted_index.inhomogeneity | 81 |
| abstract_inverted_index.perturbations | 146 |
| abstract_inverted_index.respectively. | 86 |
| abstract_inverted_index.discretization | 103 |
| abstract_inverted_index.fixed-endpoint | 11 |
| abstract_inverted_index.inhomogeneous, | 53 |
| abstract_inverted_index.interferometry. | 218 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |