Paper Info
Title
An Exact Penalty Method for Free Terminal Time Optimal Control Problem with Continuous Inequality Constraints.
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. © 2012 Springer Science+Business Media, LLC.
Year
DOI
Venue
2012
10.1007/s10957-012-0006-9
J. Optimization Theory and Applications
Keywords
Field
DocType
constrained optimization,exact penalty functions,hypersonic vehicles,nonlinear programming,optimal control
Mathematical optimization,Optimal control,Constraint (mathematics),Control function,Nonlinear programming,Inequality,Mathematics,Maximization,Constrained optimization,Penalty method
Journal
Volume
Issue
ISSN
154
1
15732878
Citations 
PageRank 
References 
11
0.93
3
Authors
5
Name
Order
Citations
PageRank
Canghua Jiang1242.78
Qun Lin2586.41
Changjun Yu3788.67
K. L. Teo41643211.47
Guang-Ren Duan51735177.31