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An Exact Penalty Method for Free Terminal Time Optimal Control Problem with Continuous Inequality Constraints

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Abstract

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.

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Acknowledgements

Research supported by China Scholarship Council, a grant from the Australian Research Council, and the Innovation Team Program of the National Science Foundation of China under Grant No. 61021002 Robust flight control theory and applications.

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Authors and Affiliations

  1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, P.R.China

    Canghua Jiang & Guang-Ren Duan

  2. Department of Mathematics and Statistics, Curtin University, Perth, 6845, Australia

    Qun Lin, Changjun Yu & Kok Lay Teo

Authors
  1. Canghua Jiang
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  2. Qun Lin
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  3. Changjun Yu
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  4. Kok Lay Teo
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  5. Guang-Ren Duan
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Corresponding author

Correspondence to Kok Lay Teo.

Additional information

Communicated by George Leitmann.

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Jiang, C., Lin, Q., Yu, C. et al. An Exact Penalty Method for Free Terminal Time Optimal Control Problem with Continuous Inequality Constraints. J Optim Theory Appl 154, 30–53 (2012). https://doi.org/10.1007/s10957-012-0006-9

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  • DOI: https://doi.org/10.1007/s10957-012-0006-9

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