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

K.L. Teo, W.R. Lee, Leslie Jennings, Song Wang, Y. Liu

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)436-478
    JournalAnziam Journal
    Volume43
    Issue number4
    Publication statusPublished - 2002

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    Optimal Control Problem
    Objective function
    Numerical Solution
    Control Parametrization
    Partition
    Piecewise Linear Function
    Control Function
    Convert
    Transform
    Parameter Selection
    Optimal Parameter
    Cost Function
    Horizon
    Gradient
    Optimization Problem
    Numerical Examples

    Cite this

    Teo, K. L., Lee, W. R., Jennings, L., Wang, S., & Liu, Y. (2002). Numerical solution of an optimal control problem with variable time points in the objective function. Anziam Journal, 43(4), 436-478.
    Teo, K.L. ; Lee, W.R. ; Jennings, Leslie ; Wang, Song ; Liu, Y. / Numerical solution of an optimal control problem with variable time points in the objective function. In: Anziam Journal. 2002 ; Vol. 43, No. 4. pp. 436-478.
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    Teo, KL, Lee, WR, Jennings, L, Wang, S & Liu, Y 2002, 'Numerical solution of an optimal control problem with variable time points in the objective function' 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.

    In: Anziam Journal, Vol. 43, No. 4, 2002, p. 436-478.

    Research output: Contribution to journalArticle

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    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.

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