Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations
For the solution of optimal control problem involving an index-1 differential-algebraic equation, an efficient function evaluation algorithm is proposed in this paper. In the evaluation procedure, the state equation is propagated forwards, then, adjoint sensitivity is propagated backwards. Thus, it...
| Main Authors: | , , , |
|---|---|
| Format: | Conference Paper |
| Published: |
2017
|
| Online Access: | http://hdl.handle.net/20.500.11937/59275 |
| _version_ | 1848760434377621504 |
|---|---|
| author | Jiang, C. Xie, K. Guo, Z. Teo, Kok Lay |
| author_facet | Jiang, C. Xie, K. Guo, Z. Teo, Kok Lay |
| author_sort | Jiang, C. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | For the solution of optimal control problem involving an index-1 differential-algebraic equation, an efficient function evaluation algorithm is proposed in this paper. In the evaluation procedure, the state equation is propagated forwards, then, adjoint sensitivity is propagated backwards. Thus, it is computationally more efficient than forward sensitivity propagation when the number of constraints is less than that of optimization variables. In order to reduce Newton iterations, the adjoint sensitivity is derived utilizing the implicit function theorem, and the integration procedure is accelerated by incorporating a predictor-corrector strategy. This algorithm is integrated with a nonlinear programming solver Ipopt to solve sequentially the point-to-point optimal control for a Delta robot with constrained motor torque. Numerical experiments demonstrate the efficiency of this algorithm. |
| first_indexed | 2025-11-14T10:15:43Z |
| format | Conference Paper |
| id | curtin-20.500.11937-59275 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:15:43Z |
| publishDate | 2017 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-592752018-05-08T06:05:23Z Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations Jiang, C. Xie, K. Guo, Z. Teo, Kok Lay For the solution of optimal control problem involving an index-1 differential-algebraic equation, an efficient function evaluation algorithm is proposed in this paper. In the evaluation procedure, the state equation is propagated forwards, then, adjoint sensitivity is propagated backwards. Thus, it is computationally more efficient than forward sensitivity propagation when the number of constraints is less than that of optimization variables. In order to reduce Newton iterations, the adjoint sensitivity is derived utilizing the implicit function theorem, and the integration procedure is accelerated by incorporating a predictor-corrector strategy. This algorithm is integrated with a nonlinear programming solver Ipopt to solve sequentially the point-to-point optimal control for a Delta robot with constrained motor torque. Numerical experiments demonstrate the efficiency of this algorithm. 2017 Conference Paper http://hdl.handle.net/20.500.11937/59275 10.23919/ChiCC.2017.8027734 fulltext |
| spellingShingle | Jiang, C. Xie, K. Guo, Z. Teo, Kok Lay Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations |
| title | Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations |
| title_full | Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations |
| title_fullStr | Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations |
| title_full_unstemmed | Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations |
| title_short | Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations |
| title_sort | implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations |
| url | http://hdl.handle.net/20.500.11937/59275 |