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

Canghua Jiang (), Qun Lin (), Changjun Yu (), Kok Lay Teo () and Guang-Ren Duan ()
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Canghua Jiang: Harbin Institute of Technology
Qun Lin: Curtin University
Changjun Yu: Curtin University
Kok Lay Teo: Curtin University
Guang-Ren Duan: Harbin Institute of Technology

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 1, No 3, 30-53

Abstract: 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.

Keywords: Optimal control; Nonlinear programming; Constrained optimization; Exact penalty functions; Hypersonic vehicles (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-012-0006-9

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