2016/08/31 by Nithin Govindarajan, Hassan Arbabi, Govindarajan, Nithin +9 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Adversarial Robustness in Machine Learning #Dynamical Systems (math.DS) #FOS: Mathematics #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.1608.08734
openalex publication_date 2016/08/31 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We apply an operator-theoretic viewpoint to a class of non-smooth dynamical\nsystems that are exposed to event-triggered state resets. The considered\nbenchmark problem is that of a pendulum which receives a downward kick under\ncertain fixed angles. The pendulum is modeled as a hybrid automaton and is\nanalyzed from both a geometric perspective and the formalism carried out by\nKoopman operator theory. A connection is drawn between these two\ninterpretations of a dynamical system by means of establishing a link between\nthe spectral properties of the Koopman operator and the geometric properties in\nthe state-space.\n