Numerical Optimal Control for Differential Equations with State Dependent Switches and Jumps

Armin Nurkanović

University of Freiburg

Tuesday, July 05, 2022, 14:15

Seminarraum 226, Rechenzentrum, Hermann-Herder-Str 10

Optimal control problems for dynamical systems with state dependent switches are inherently non-smooth and non-convex and therefore difficult to treat numerically.  Systems with state dependent jumps are even more difficult to treat than systems with switches, as they lead to discontinuous state trajectories. We present two recently developed ideas: First, the method of Finite Elements with Switch Detection (FESD) to numerically solve optimal control problems of switched systems with high order of accuracy.  Second, the time-freezing idea for optimal control problems with state jumps, which allows one to reformulate these problems into the easier class of problems with switches, which can then be treated by the FESD method. Both methods are illustrated with numerical examples including the challenging optimal control problem of a hopping robot with ground contact and friction that should detect an optimal jump sequence to a final position in the presence of holes.