### Abstract

Original language | English |
---|---|

Pages (from-to) | 436-478 |

Journal | Anziam Journal |

Volume | 43 |

Issue number | 4 |

Publication status | Published - 2002 |

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### Cite this

*Anziam Journal*,

*43*(4), 436-478.

}

*Anziam Journal*, vol. 43, no. 4, pp. 436-478.

**Numerical solution of an optimal control problem with variable time points in the objective function.** / Teo, K.L.; Lee, W.R.; Jennings, Leslie; Wang, Song; Liu, Y.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Numerical solution of an optimal control problem with variable time points in the objective function

AU - Teo, K.L.

AU - Lee, W.R.

AU - Jennings, Leslie

AU - Wang, Song

AU - Liu, Y.

PY - 2002

Y1 - 2002

N2 - In this paper, we consider the numerical solution of a class of optimal control problems involving variable time points in their cost functions. The control enhancing transform is first used to convert the optimal control problem with variable time points into an equivalent optimal control problem with fixed multiple characteristic time (MCT). Using the control parametrization technique, the time horizon is partitioned into several subintervals. Let the partition points also be taken as decision variables. The control functions are approximated by piecewise constant or piecewise linear functions in accordance with these variable partition points. We thus obtain a finite dimensional optimization problem. The control parametrization enhancing control transform (CPET) is again used to convert approximate optimal control problems with variable partition points into equivalent standard optimal control problems with MCT, where the control functions are piecewise constant or piecewise linear functions with pre-fixed partition points. The transformed problems are essentially optimal parameter selection problems with MCT. The gradient formulae for the objective function as well as the constraint functions with respect to relevant decision variables are obtained. Numerical examples are solved using the proposed method.

AB - In this paper, we consider the numerical solution of a class of optimal control problems involving variable time points in their cost functions. The control enhancing transform is first used to convert the optimal control problem with variable time points into an equivalent optimal control problem with fixed multiple characteristic time (MCT). Using the control parametrization technique, the time horizon is partitioned into several subintervals. Let the partition points also be taken as decision variables. The control functions are approximated by piecewise constant or piecewise linear functions in accordance with these variable partition points. We thus obtain a finite dimensional optimization problem. The control parametrization enhancing control transform (CPET) is again used to convert approximate optimal control problems with variable partition points into equivalent standard optimal control problems with MCT, where the control functions are piecewise constant or piecewise linear functions with pre-fixed partition points. The transformed problems are essentially optimal parameter selection problems with MCT. The gradient formulae for the objective function as well as the constraint functions with respect to relevant decision variables are obtained. Numerical examples are solved using the proposed method.

M3 - Article

VL - 43

SP - 436

EP - 478

JO - Anziam Journal

JF - Anziam Journal

SN - 1446-1811

IS - 4

ER -