Superlinear Convergence Using Controls Based on Second-Order Needle Variations

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper investigates the convergence performance of second-order needle variation methods for nonlinear control-affine systems. Control solutions have a closed-form expression that is derived from the first-and second-order mode insertion gradients of the objective and are proven to exhibit superlinear convergence near equilibrium. Compared to first-order needle variations, the proposed synthesis scheme exhibits superior convergence at smaller computational cost than alternative nonlinear feedback controllers. Simulation results on the differential drive model verify the analysis and show that second-order needle variations outperform first-order variational methods and iLQR near the optimizer. Last, even when implemented in a closed-loop, receding horizon setting, the proposed algorithm demonstrates superior convergence against the iterative linear quadratic Gaussian (iLQG) controller.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4301-4308
Number of pages8
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Superlinear Convergence
Needles
First-order
Controller
Nonlinear Alternative
Nonlinear feedback
Controllers
Affine Systems
Nonlinear Control
Variational Methods
Closed-loop
Insertion
Computational Cost
Horizon
Closed-form
Control System
Synthesis
Verify
Gradient
Demonstrate

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Mamakoukas, G., MacIver, M. A., & Murphey, T. D. (2019). Superlinear Convergence Using Controls Based on Second-Order Needle Variations. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 4301-4308). [8619405] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619405
Mamakoukas, Giorgos ; MacIver, Malcolm Angus ; Murphey, Todd David. / Superlinear Convergence Using Controls Based on Second-Order Needle Variations. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 4301-4308 (Proceedings of the IEEE Conference on Decision and Control).
@inproceedings{be073726e945428181a66db1f736a81c,
title = "Superlinear Convergence Using Controls Based on Second-Order Needle Variations",
abstract = "This paper investigates the convergence performance of second-order needle variation methods for nonlinear control-affine systems. Control solutions have a closed-form expression that is derived from the first-and second-order mode insertion gradients of the objective and are proven to exhibit superlinear convergence near equilibrium. Compared to first-order needle variations, the proposed synthesis scheme exhibits superior convergence at smaller computational cost than alternative nonlinear feedback controllers. Simulation results on the differential drive model verify the analysis and show that second-order needle variations outperform first-order variational methods and iLQR near the optimizer. Last, even when implemented in a closed-loop, receding horizon setting, the proposed algorithm demonstrates superior convergence against the iterative linear quadratic Gaussian (iLQG) controller.",
author = "Giorgos Mamakoukas and MacIver, {Malcolm Angus} and Murphey, {Todd David}",
year = "2019",
month = "1",
day = "18",
doi = "10.1109/CDC.2018.8619405",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "4301--4308",
booktitle = "2018 IEEE Conference on Decision and Control, CDC 2018",
address = "United States",

}

Mamakoukas, G, MacIver, MA & Murphey, TD 2019, Superlinear Convergence Using Controls Based on Second-Order Needle Variations. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619405, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 4301-4308, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619405

Superlinear Convergence Using Controls Based on Second-Order Needle Variations. / Mamakoukas, Giorgos; MacIver, Malcolm Angus; Murphey, Todd David.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 4301-4308 8619405 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Superlinear Convergence Using Controls Based on Second-Order Needle Variations

AU - Mamakoukas, Giorgos

AU - MacIver, Malcolm Angus

AU - Murphey, Todd David

PY - 2019/1/18

Y1 - 2019/1/18

N2 - This paper investigates the convergence performance of second-order needle variation methods for nonlinear control-affine systems. Control solutions have a closed-form expression that is derived from the first-and second-order mode insertion gradients of the objective and are proven to exhibit superlinear convergence near equilibrium. Compared to first-order needle variations, the proposed synthesis scheme exhibits superior convergence at smaller computational cost than alternative nonlinear feedback controllers. Simulation results on the differential drive model verify the analysis and show that second-order needle variations outperform first-order variational methods and iLQR near the optimizer. Last, even when implemented in a closed-loop, receding horizon setting, the proposed algorithm demonstrates superior convergence against the iterative linear quadratic Gaussian (iLQG) controller.

AB - This paper investigates the convergence performance of second-order needle variation methods for nonlinear control-affine systems. Control solutions have a closed-form expression that is derived from the first-and second-order mode insertion gradients of the objective and are proven to exhibit superlinear convergence near equilibrium. Compared to first-order needle variations, the proposed synthesis scheme exhibits superior convergence at smaller computational cost than alternative nonlinear feedback controllers. Simulation results on the differential drive model verify the analysis and show that second-order needle variations outperform first-order variational methods and iLQR near the optimizer. Last, even when implemented in a closed-loop, receding horizon setting, the proposed algorithm demonstrates superior convergence against the iterative linear quadratic Gaussian (iLQG) controller.

UR - http://www.scopus.com/inward/record.url?scp=85062189999&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062189999&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8619405

DO - 10.1109/CDC.2018.8619405

M3 - Conference contribution

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4301

EP - 4308

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -

Mamakoukas G, MacIver MA, Murphey TD. Superlinear Convergence Using Controls Based on Second-Order Needle Variations. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 4301-4308. 8619405. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8619405