An Implementation of the Universal Birkhoff Pseudospectral Theory Using a Generic Nonlinear Programming Solver

Chenyang Liu; Junhui Liu; Jiayuan Shan; Chunyu Li; Jianan Wang; Yankai Wang

doi:10.1109/ICCA69928.2026.11618044

An Implementation of the Universal Birkhoff Pseudospectral Theory Using a Generic Nonlinear Programming Solver

Chenyang Liu
, Junhui Liu^*
, Jiayuan Shan
, Chunyu Li
, Jianan Wang
, Yankai Wang

^*Corresponding author for this work

Beijing Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We implement the universal Birkhoff pseudospectral theory over Legendre-Gauss-Radau grid by developing new covector mapping theorem for generic nonlinear programming algorithms. Considering the barriers between the stationarity conditions and optimality, we utilize the tightened Birkhoff theories specifically for nonlinear programming implementations to augment and relax primal conditions, and the relating covector mapping theorem is constructed with the specially modified Lagrangian. Examples of singular optimal control problem are provided, demonstrating the effectiveness and potential generality of our new theories for implementations.

Original language	English
Title of host publication	2026 IEEE 20th International Conference on Control and Automation, ICCA 2026
Publisher	IEEE Computer Society
Pages	2062-2069
Number of pages	8
ISBN (Electronic)	9798331548537
DOIs	https://doi.org/10.1109/ICCA69928.2026.11618044
Publication status	Published - 2026
Externally published	Yes
Event	20th IEEE International Conference on Control and Automation, ICCA 2026 - Almaty, Kazakhstan Duration: 16 Jun 2026 → 19 Jun 2026

Publication series

Name	IEEE International Conference on Control and Automation, ICCA
ISSN (Print)	1948-3449
ISSN (Electronic)	1948-3457

Conference

Conference	20th IEEE International Conference on Control and Automation, ICCA 2026
Country/Territory	Kazakhstan
City	Almaty
Period	16/06/26 → 19/06/26

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10.1109/ICCA69928.2026.11618044

Cite this

Liu, C., Liu, J., Shan, J., Li, C., Wang, J., & Wang, Y. (2026). An Implementation of the Universal Birkhoff Pseudospectral Theory Using a Generic Nonlinear Programming Solver. In 2026 IEEE 20th International Conference on Control and Automation, ICCA 2026 (pp. 2062-2069). (IEEE International Conference on Control and Automation, ICCA). IEEE Computer Society. https://doi.org/10.1109/ICCA69928.2026.11618044

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title = "An Implementation of the Universal Birkhoff Pseudospectral Theory Using a Generic Nonlinear Programming Solver",

abstract = "We implement the universal Birkhoff pseudospectral theory over Legendre-Gauss-Radau grid by developing new covector mapping theorem for generic nonlinear programming algorithms. Considering the barriers between the stationarity conditions and optimality, we utilize the tightened Birkhoff theories specifically for nonlinear programming implementations to augment and relax primal conditions, and the relating covector mapping theorem is constructed with the specially modified Lagrangian. Examples of singular optimal control problem are provided, demonstrating the effectiveness and potential generality of our new theories for implementations.",

author = "Chenyang Liu and Junhui Liu and Jiayuan Shan and Chunyu Li and Jianan Wang and Yankai Wang",

note = "Publisher Copyright: {\textcopyright} 2026 IEEE.; 20th IEEE International Conference on Control and Automation, ICCA 2026 ; Conference date: 16-06-2026 Through 19-06-2026",

year = "2026",

doi = "10.1109/ICCA69928.2026.11618044",

language = "English",

series = "IEEE International Conference on Control and Automation, ICCA",

publisher = "IEEE Computer Society",

pages = "2062--2069",

booktitle = "2026 IEEE 20th International Conference on Control and Automation, ICCA 2026",

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Liu, C, Liu, J , Shan, J, Li, C, Wang, J & Wang, Y 2026, An Implementation of the Universal Birkhoff Pseudospectral Theory Using a Generic Nonlinear Programming Solver. in 2026 IEEE 20th International Conference on Control and Automation, ICCA 2026. IEEE International Conference on Control and Automation, ICCA, IEEE Computer Society, pp. 2062-2069, 20th IEEE International Conference on Control and Automation, ICCA 2026, Almaty, Kazakhstan, 16/06/26. https://doi.org/10.1109/ICCA69928.2026.11618044

An Implementation of the Universal Birkhoff Pseudospectral Theory Using a Generic Nonlinear Programming Solver. / Liu, Chenyang; Liu, Junhui ; Shan, Jiayuan et al.
2026 IEEE 20th International Conference on Control and Automation, ICCA 2026. IEEE Computer Society, 2026. p. 2062-2069 (IEEE International Conference on Control and Automation, ICCA).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - An Implementation of the Universal Birkhoff Pseudospectral Theory Using a Generic Nonlinear Programming Solver

AU - Liu, Chenyang

AU - Liu, Junhui

AU - Shan, Jiayuan

AU - Li, Chunyu

AU - Wang, Jianan

AU - Wang, Yankai

PY - 2026

Y1 - 2026

N2 - We implement the universal Birkhoff pseudospectral theory over Legendre-Gauss-Radau grid by developing new covector mapping theorem for generic nonlinear programming algorithms. Considering the barriers between the stationarity conditions and optimality, we utilize the tightened Birkhoff theories specifically for nonlinear programming implementations to augment and relax primal conditions, and the relating covector mapping theorem is constructed with the specially modified Lagrangian. Examples of singular optimal control problem are provided, demonstrating the effectiveness and potential generality of our new theories for implementations.

AB - We implement the universal Birkhoff pseudospectral theory over Legendre-Gauss-Radau grid by developing new covector mapping theorem for generic nonlinear programming algorithms. Considering the barriers between the stationarity conditions and optimality, we utilize the tightened Birkhoff theories specifically for nonlinear programming implementations to augment and relax primal conditions, and the relating covector mapping theorem is constructed with the specially modified Lagrangian. Examples of singular optimal control problem are provided, demonstrating the effectiveness and potential generality of our new theories for implementations.

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U2 - 10.1109/ICCA69928.2026.11618044

DO - 10.1109/ICCA69928.2026.11618044

M3 - Conference contribution

AN - SCOPUS:105047317850

T3 - IEEE International Conference on Control and Automation, ICCA

SP - 2062

EP - 2069

BT - 2026 IEEE 20th International Conference on Control and Automation, ICCA 2026

PB - IEEE Computer Society

T2 - 20th IEEE International Conference on Control and Automation, ICCA 2026

Y2 - 16 June 2026 through 19 June 2026

ER -

Liu C, Liu J , Shan J, Li C, Wang J , Wang Y. An Implementation of the Universal Birkhoff Pseudospectral Theory Using a Generic Nonlinear Programming Solver. In 2026 IEEE 20th International Conference on Control and Automation, ICCA 2026. IEEE Computer Society. 2026. p. 2062-2069. (IEEE International Conference on Control and Automation, ICCA). doi: 10.1109/ICCA69928.2026.11618044

An Implementation of the Universal Birkhoff Pseudospectral Theory Using a Generic Nonlinear Programming Solver

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