Moritz Diehl, K.U. Leuven
Abstract:
When nonlinear dynamic systems shall be controlled to perform certain tasks optimally, nonlinear optimal control problems have to solved which are necessarily non-convex. Often it is even desired to solve such problems in real-time, each time for modified problem data.
This occurs most prominently in the framework of "model predictive control", where an optimization based feedback law is generated, and where the evolving problem data are the most current state estimates available for the system being controlled.
We first briefly review the state-of-the-art in nonlinear dynamic optimization and point out the differences between approaches based on Sequential Quadratic Programming (SQP) and Interior-Point (IP) methods, and then discuss algorithmic ideas that have been developed in order to address the real-time challenges, and which sacrifice accuracy for computational speed yet are still able to offer convergence guarantees for the closed loop system.
We finally discuss several simulated and experimental applications from mechatronics where the different algorithms have been used, among them robot arms that shall move in minimal time and power generating kite systems.