An exact penalty method for free terminal time optimal control problem with continuous inequality constraints (Q1762391)

The authors consider a class of optimal control problems with free terminal time and continuous inequality constraints. They approximate the control function with a piecewise-constant function and transform the inequality constraints into terminal equality constraints for an auxiliary differential system. The constraint optimization problem is transformed into a penalized problem with only box constraints on the decision variables using a novel exact penalty function. This penalized problem is solved by a gradient-based optimization technique. They show that this penalty function has continuous derivatives. For a sufficiently large and finite parameter, its local minimizer is feasible and also local minimizer of the constrained problem. Numerical simulations have been also performed.