A differential dynamic programming method with an abrupt penalty integrand for solving tolerance problems

A non-linear optimal control problem is considered in respect to a new class of performance index. The problem is to control an output function to be inside a prescribed tolerance zone. When inside the zone, this will result in a favourable cost contribution. When outside there will be no contribution. The numerical optimization algorithm used is a modified differential dynamic programming method. The method is expanded to this class of cost functionals. An example illustrates the difference in using the new cost functional and two other commonly used cost functionals.