A technique for improving numerical stability and efficiency in singular control problems

A new method for the numerical treatment of optimal control problems with first order singular control is proposed. The basic idea of this method is to build a closed loop type control that stabilizes the system on the singular manifold. As a standard technique, the singular control is computed with the use of additional optimality conditions. This technique may imply numerical problems which in some cases are so significant that it becomes impossible to solve the optimal control problem. The proposed method yields a solution for this problem. It can be implemented easily using standard software for integrating the system. The optimal control problem is transformed to a boundary value problem using the minimum principle. Choosing appropriate values for the feedback factors of the closed loop system leads to improved convergence characteristics of the multiple shooting algorithm applied for solving the associated boundary value problem.