2019/01/09 by Christoph Kawan, Serdar Yüksel, Kawan, Christoph +1
Biochemistry, Genetics and Molecular Biology · Engineering · #37A35 #93C10 #93E15 #Advanced Control Systems Optimization #Control Systems and Identification #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Information Theory (cs.IT) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1901.02825
openalex publication_date 2019/01/09 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
Given a stochastic nonlinear system controlled over a possibly noisy\ncommunication channel, the paper studies the largest class of channels for\nwhich there exist coding and control policies so that the closed-loop system is\nstochastically stable. The stability criterion considered is asymptotic mean\nstationarity (AMS). We develop a general method based on ergodic theory and\nprobability to derive fundamental bounds on information transmission\nrequirements leading to stabilization. Through this method we develop a new\nnotion of entropy which is tailored to derive lower bounds for asymptotic mean\nstationarity for both noise-free and noisy channels. The bounds obtained\nthrough probabilistic and ergodic-theoretic analysis are more refined in\ncomparison with the bounds obtained earlier via information-theoretic methods.\nMoreover, our approach is more versatile in view of the models considered and\nallows for finer lower bounds when the AMS measure is known to admit further\nproperties such as moment bounds.\n