{'fraction_non_alphanumeric': 0.010924369747899159, 'fraction_numerical': 0.0, 'mean_word_length': 5.580110497237569, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Constructive approximations of the Zeno dynamics in affine switched systems: The projection based approach

This paper deals with a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno dynamics. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real-world processes do not present the corresponding behavior, mathematical models of some interconnected engineering systems may be Zeno due to the corresponding formal abstraction. We propose a useful approximative approach to Zeno dynamics, namely, a projection based characterization of this phenomena. A resulting trajectory associated with the Zeno dynamics can finally be described as a result of a specific dynamic projection procedure applied to the original model. We use here the projected dynamic systems methodology. The obtained formal description provides an effective theoretic basis for a constructive treatment of the Zeno behaviour. We also discuss an application of the proposed technique to the conventional sliding mode control processes.