Discontinuous control systems

By means of some simple examples from economics, we elucidatecertain solution tools for the solution of optimal control problems were the system under study undergoes major changes when certain boundaries are crossed. The "major changes" may be that the state gets a jump discontinuity when crossing a boundary, or that the right hand side of the differential equation changes. Some theoretical result are presented. Among the results presented, at least the sufficient condition related to fields of extremals should be new.