Olaf Stursberg

Nils Hanke, Zonglin Liu, Olaf Stursberg

This paper introduces a novel method to approximate limit cycles of nonlinear ODEs by use of switching affine dynamics in order to ease data-based modeling and analysis. Previous approaches to approximating limit cycles by switching systems have been largely confined to simple partitions into two-regions or low-dimensional (often planar) settings. In contrast, this study utilizes more general partitions in higher-dimensional state spaces, augmented by external signals, to develop a synthesis scheme that guarantees a globally stable limit cycle. The synthesis task is formulated and solved based on constrained numerical optimization. Starting from sampled data of the nonlinear dynamics, the method minimizes the error between the data and the limit cycle generated by the switching affine model, while employing stability constraints to ensure global stability. Based on the obtained model, the paper tackles the problem of reference tracking for switching affine systems with periodic behavior. While the approximation scheme is based on a common Lyapunov function, the reference tracking approach uses multiple Lyapunov functions to achieve less conservative convergence results. The principle and effectiveness of the proposed methods are illustrated through a set of examples.

Jannik Hahn, Richard Schoeffauer, Gerhard Wunder et al.

The novel idea presented in this paper is to interweave distributed model predictive control with a reliable scheduling of the information that is interchanged between local controllers of the plant subsystems. To this end, a dynamic model of the communication network and a predictive scheduling algorithm are proposed, the latter providing predictions of the delay between sending and receiving information. These predictions can be used by the local subsystem controllers to improve their control performance, as exemplary shown for a platooning example.