Remote state estimation problem: Towards the data-rate limit along the avenue of the second Lyapunov method. (March 2021)

• Record Type: Journal Article
• Authors: Kawan, Christoph; Matveev, Alexey S.; Pogromsky, Alexander Yu.
• Is Part Of: Automatica. Volume 125(2021)
• Publication Date: 2021-03
• Subjects: Entropy -- Nonlinear systems -- First and second Lyapunov methods -- Remote state estimation -- Finite bit-rates; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2020.109467
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which the state of a system can be estimated so that the estimation quality does not degrade over time and, conversely, can be improved. The remote observer here is assumed to receive its data through a communication channel of finite bit-rate capacity. In this paper, we provide a new characterization of the restoration entropy which does not require to compute any temporal limit, i.e., an asymptotic quantity. Our new formula is based on the idea of finding a specific Riemannian metric on the state space which makes the metric-dependent upper estimate of the restoration entropy as tight as one wishes.