An exact penalty method for free terminal time optimal control problem with continuous inequality constraints
In this paper, we consider a class of optimal control problems with free terminal time and continuous inequality constraints. First, the problem is approximated by representing the control function as a piecewise-constant function. Then the continuous inequality constraints are transformed into term...
| Main Authors: | , , , , |
|---|---|
| Format: | Journal Article |
| Published: |
Springer Netherlands
2012
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/14871 |
| _version_ | 1848748739535044608 |
|---|---|
| author | Jiang, Canghua Lin, Qun Yu, Changjun Teo, Kok Lay Duan, Guang-Ren |
| author_facet | Jiang, Canghua Lin, Qun Yu, Changjun Teo, Kok Lay Duan, Guang-Ren |
| author_sort | Jiang, Canghua |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider a class of optimal control problems with free terminal time and continuous inequality constraints. First, the problem is approximated by representing the control function as a piecewise-constant function. Then the continuous inequality constraints are transformed into terminal equality constraints for an auxiliary differential system. After these two steps, we transform the constrained optimization problem into a penalized problem with only box constraints on the decision variables using a novel exact penalty function. This penalized problem is then solved by a gradient-based optimization technique. Theoretical analysis proves that this penalty function has continuous derivatives, and for a sufficiently large and finite penalty parameter, its local minimizer is feasible in the sense that the continuous inequality constraints are satisfied. Furthermore, this local minimizer is also the local minimizer of the constrained problem. Numerical simulations on the range maximization for a hypersonic vehicle reentering the atmosphere subject to a heating constraint demonstrate the effectiveness of our method. |
| first_indexed | 2025-11-14T07:09:50Z |
| format | Journal Article |
| id | curtin-20.500.11937-14871 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:09:50Z |
| publishDate | 2012 |
| publisher | Springer Netherlands |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-148712017-09-13T15:01:40Z An exact penalty method for free terminal time optimal control problem with continuous inequality constraints Jiang, Canghua Lin, Qun Yu, Changjun Teo, Kok Lay Duan, Guang-Ren Hypersonic vehicles Constrained optimization Nonlinear programming Exact penalty functions Optimal control In this paper, we consider a class of optimal control problems with free terminal time and continuous inequality constraints. First, the problem is approximated by representing the control function as a piecewise-constant function. Then the continuous inequality constraints are transformed into terminal equality constraints for an auxiliary differential system. After these two steps, we transform the constrained optimization problem into a penalized problem with only box constraints on the decision variables using a novel exact penalty function. This penalized problem is then solved by a gradient-based optimization technique. Theoretical analysis proves that this penalty function has continuous derivatives, and for a sufficiently large and finite penalty parameter, its local minimizer is feasible in the sense that the continuous inequality constraints are satisfied. Furthermore, this local minimizer is also the local minimizer of the constrained problem. Numerical simulations on the range maximization for a hypersonic vehicle reentering the atmosphere subject to a heating constraint demonstrate the effectiveness of our method. 2012 Journal Article http://hdl.handle.net/20.500.11937/14871 10.1007/s10957-012-0006-9 Springer Netherlands restricted |
| spellingShingle | Hypersonic vehicles Constrained optimization Nonlinear programming Exact penalty functions Optimal control Jiang, Canghua Lin, Qun Yu, Changjun Teo, Kok Lay Duan, Guang-Ren An exact penalty method for free terminal time optimal control problem with continuous inequality constraints |
| title | An exact penalty method for free terminal time optimal control problem with continuous inequality constraints |
| title_full | An exact penalty method for free terminal time optimal control problem with continuous inequality constraints |
| title_fullStr | An exact penalty method for free terminal time optimal control problem with continuous inequality constraints |
| title_full_unstemmed | An exact penalty method for free terminal time optimal control problem with continuous inequality constraints |
| title_short | An exact penalty method for free terminal time optimal control problem with continuous inequality constraints |
| title_sort | exact penalty method for free terminal time optimal control problem with continuous inequality constraints |
| topic | Hypersonic vehicles Constrained optimization Nonlinear programming Exact penalty functions Optimal control |
| url | http://hdl.handle.net/20.500.11937/14871 |