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 language | English (US) |
|---|---|
| Title of host publication | 2018 IEEE Conference on Decision and Control, CDC 2018 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 4301-4308 |
| Number of pages | 8 |
| ISBN (Electronic) | 9781538613955 |
| DOIs | |
| State | Published - Jan 18 2019 |
| Event | 57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: Dec 17 2018 → Dec 19 2018 |
Publication series
| Name | Proceedings of the IEEE Conference on Decision and Control |
|---|---|
| Volume | 2018-December |
| ISSN (Print) | 0743-1546 |
Conference
| Conference | 57th IEEE Conference on Decision and Control, CDC 2018 |
|---|---|
| Country | United States |
| City | Miami |
| Period | 12/17/18 → 12/19/18 |
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ASJC Scopus subject areas
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization
Cite this
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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 proceeding › Conference 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 -