Invariance Properties of Controlled Stochastic Nonlinear Systems Under Information Constraints

• 成果类型: Article
• 署名作者: Kawan, Christoph; Yuksel, Serdar
• 署名单位: University of Munich; Queens University - Canada
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3030846
• 发表日期: 2021
• 页码: 4514-4529
• 关键词: entropy; Stability criteria; Nonlinear systems; asymptotic stability; Stochastic processes; Noise measurement; control systems; Asymptotic mean stationarity (AMS); Information theory; Networked control; stochastic stabilization

摘要

Given a stochastic nonlinear system controlled over a possibly noisy communication channel, the article studies the largest class of channels for which there exist coding and control policies so that the closed-loop system is stochastically stable. The stability criterion considered is asymptotic mean stationarity (AMS). In this article, we develop a general method based on ergodic theory and probability to derive fundamental bounds on information transmission requirements leading to stabilization. Through this method, we develop a new notion of entropy which is tailored to derive lower bounds for AMS for both noise-free and noisy channels. The bounds obtained through probabilistic and ergodic-theoretic analysis are more refined in comparison with the bounds obtained earlier via information-theoretic methods. Moreover, our approach is more versatile in view of the models considered and allows for finer lower bounds when the AMS measure is known to admit further properties, such as moment bounds.