Discontinuity of the Costates for Optimal Control Problems with Columb Friction

摘要

This work points out that the costates are actually discontinuous functions of time for optimal control problems with Coloumb friction. In particular these discontinuities occur at the time points where the velocity of the system changes sign. To the authors knowledge, this has not been noted before. This phenomenon is demonstrated on a minimum-time problem with Coloumb friction and the consistency of discontinuous costates and switching functions with respect to the input switches is shown.