The reduced system method for control problems with kinks

A method is developed for solving optimal-control problems having cost functionals or system functions that are continuous but, have discontinuous partial derivatives with respect to the state variables. The method is based on splitting the total time interval on which the problem is defined into segments where the trajectory either totally avoids the points of discontinuity or stays fixed at such a point. Examples are given which motivate consideration of such problems and illustrate the proposed method of solution. © 1974 Taylor & Francis Group, LLC.