This talk presents a novel reformulation and numerical methods for optimal control of dynamical systems with state jumps. The systems with state jumps are transformed into piecewise smooth systems. The main idea of the time-freezing reformulation is to introduce a clock state and an auxiliary dynamic system whose trajectory endpoints satisfy the state jump law. When the auxiliary system is active, the clock state is not evolving, hence by taking only the parts of thetrajectory when the clock state was active, we can recover the original solution. We show how the time-freezing reformulation can be used for mechanical systems with friction and impacts (both elastic and inelastic) and for hybrid systems with hysteresis. We detail how to recover the solution of the original system and show how to select appropriate auxiliary dynamics. For numerically solving optimal control problems one can apply the recently proposed Finite Elements with Switch Detection (FESD) method. This enables the treatment of a broad class of nonsmooth systems in a unified way.
The talk is based on joint work with Armin Nurkanovic, Stefan Albrecht,Tommaso Sartor, and Bernard Brogliato.
Moritz Diehl was born in Hamburg, Germany, in 1971. He studied physics and mathematics at Heidelberg and Cambridge University from 1993-1999, and received his Ph.D. degree from Heidelberg University in 2001, at the Interdisciplinary Center for Scientific Computing. From 2006 to 2013, he was a professor with the Department of Electrical Engineering, KU Leuven University Belgium, and served as the Principal Investigator of KU Leuven's Optimization in Engineering Center OPTEC. In 2013 he moved to the University of Freiburg, Germany, where he heads the Systems Control and Optimization Laboratory, in the Department of Microsystems Engineering (IMTEK), and is also affiliated to the Department of Mathematics. His research interests are in optimization and control, spanning from numerical method development to applications in different branches of engineering, with a focus on embedded and on renewable energy systems.