Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine
The numerical solution of optimal control problems by direct collocation is a widely used approach. Quasi-Newton approximations of the Hessian of the Lagrangian of the resulting nonlinear program are also common practice. We illustrate that the transcribed problem is separable with respect to the pr...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/341716 |
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| author | Jonas Asprion Oscar Chinellato Lino Guzzella |
| author_facet | Jonas Asprion Oscar Chinellato Lino Guzzella |
| author_sort | Jonas Asprion |
| collection | DOAJ |
| description | The numerical solution of optimal control problems by direct collocation is a widely used approach. Quasi-Newton approximations of the Hessian of the Lagrangian of the resulting nonlinear program are also common practice. We illustrate that the transcribed problem is separable with respect to the primal variables and propose the application of dense quasi-Newton updates to the small diagonal blocks of the Hessian. This approach resolves memory limitations, preserves the correct sparsity pattern, and generates more accurate curvature information. The effectiveness of this improvement when applied to engineering problems is demonstrated. As an example, the fuel-optimal and emission-constrained control of a turbocharged diesel engine is considered. First results indicate a significantly faster convergence of the nonlinear program solver when the method proposed is used instead of the standard quasi-Newton approximation. |
| format | Article |
| id | doaj-art-e63c407f8bd144d0ae6aec19dc7fc0fc |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e63c407f8bd144d0ae6aec19dc7fc0fc2025-02-03T05:51:22ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/341716341716Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel EngineJonas Asprion0Oscar Chinellato1Lino Guzzella2Institute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, SwitzerlandFPT Motorenforschung AG, Schlossgasse 2, 9320 Arbon, SwitzerlandInstitute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, SwitzerlandThe numerical solution of optimal control problems by direct collocation is a widely used approach. Quasi-Newton approximations of the Hessian of the Lagrangian of the resulting nonlinear program are also common practice. We illustrate that the transcribed problem is separable with respect to the primal variables and propose the application of dense quasi-Newton updates to the small diagonal blocks of the Hessian. This approach resolves memory limitations, preserves the correct sparsity pattern, and generates more accurate curvature information. The effectiveness of this improvement when applied to engineering problems is demonstrated. As an example, the fuel-optimal and emission-constrained control of a turbocharged diesel engine is considered. First results indicate a significantly faster convergence of the nonlinear program solver when the method proposed is used instead of the standard quasi-Newton approximation.http://dx.doi.org/10.1155/2014/341716 |
| spellingShingle | Jonas Asprion Oscar Chinellato Lino Guzzella Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine Journal of Applied Mathematics |
| title | Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine |
| title_full | Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine |
| title_fullStr | Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine |
| title_full_unstemmed | Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine |
| title_short | Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine |
| title_sort | partitioned quasi newton approximation for direct collocation methods and its application to the fuel optimal control of a diesel engine |
| url | http://dx.doi.org/10.1155/2014/341716 |
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