Transformation Methods of an Exponential Function Type for the Optimal Control Problems with Constraints : 1st Report, A Method with One Correcting Parameter

Abstract

The purpose of this paper is to present a numerical method for the optimal control problems with inequality constraints. In this method such problems are solved by converting them to a sequence of problems without inequalities and by searching for the saddle point of the unconstrained function. The features in this method are as follows. 1. The optimal value of parameter is closely related to the optimal Lagrange multiplier. 2. The optimal solution is obtained as a finite value of the parameter. Thus, the fact does not yield an ill-conditioning for the penalty function in this method, as opposed to the penalty methods. 3. On account of the existence of the saddle point this method is superior to the ordinary Lagrange method. 4. This method can approach the optimal solution from the interior or exterior of constraints by choosing a parameter corresponding to the Lagrange multiplier. This method has been successfully applied to the problem with state inequality constraint.