Semi-Smooth Newton Methods for the Time Optimal Control of Nonautonomous Ordinary Differential Equations

Abstract

The control problem of minimal time transition between two stationary points are formulated in a framework of an indirect numerical method. The problem is regularized and the monotone behavior of the regularisation procedure is investigated. Semi-smooth Newton method applied on the regularized problems converge superlinearly and usually produce a very accurate solution. Differently from other methods, this one does not need a-priory knowledge of the control switching structure. A code was developed in the C++ language and the NVIDIA CUDA technology made it even faster.