State Jump Optimization for a Class of Hybrid Autonomous Systems

In this contribution, optimization of state jumps for a class of hybrid systems is considered. Basically, the control variables to be determined are the amounts of jump in the continuous states such that a corresponding cost functional is minimized. Based on a variational approach, necessary conditions of optimality are first established. The problem is then cast as a parametric optimization problem where the gradient information is derived. Finally and under some assumptions, convergence to the optimal solution of a conceptual algorithm is established. A brief discussion on the main implementation issues is also included.