A Penalty Shifting Method for Constrained Optimal Control Problems

Abstract

For nonlinear programing problems with equality constraints, Powell has proposed a new sequential unconstrained method. This paper extends the method to the optimal control problems with both equality and inequality constraints. The following results are obtained. 1. The convergence of the method is proved under a few assumptions. 2. The optimal solution is obtained as finite values of parameters. Therefore, numerical difficulties can be avoided in the minimization of the penalty function. 3. The optimal values of parameters are closely related to the optimal Lagrange multipliers. 4. The convergence to the optimal solution can be forced to be rapid by increasing the parameters corresponding to penalty coefficients. Finally, The efficiency and the accuracy of this method are investigated on a problem.