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Entropy 2019, 21(3), 282; https://doi.org/10.3390/e21030282

Data-Rate Constrained Observers of Nonlinear Systems

1
Department of Mechanical Engineering, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands
2
Department of Control Systems and Robotics, Saint Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO), 197101 Saint Petersburg, Russia
3
Department of Mathematics and Mechanics, Saint Petersburg State University, 198504 Saint Petersburg, Russia
*
Author to whom correspondence should be addressed.
Current address: Department of Mechanical Engineering, Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, The Netherlands.
Received: 15 January 2019 / Revised: 6 March 2019 / Accepted: 7 March 2019 / Published: 14 March 2019
(This article belongs to the Special Issue Entropy in Networked Control)
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Abstract

In this paper, the design of a data-rate constrained observer for a dynamical system is presented. This observer is designed to function both in discrete time and continuous time. The system is connected to a remote location via a communication channel which can transmit limited amounts of data per unit of time. The objective of the observer is to provide estimates of the state at the remote location through messages that are sent via the channel. The observer is designed such that it is robust toward losses in the communication channel. Upper bounds on the required communication rate to implement the observer are provided in terms of the upper box dimension of the state space and an upper bound on the largest singular value of the system’s Jacobian. Results that provide an analytical bound on the required minimum communication rate are then presented. These bounds are obtained by using the Lyapunov dimension of the dynamical system rather than the upper box dimension in the rate. The observer is tested through simulations for the Lozi map and the Lorenz system. For the Lozi map, the Lyapunov dimension is computed. For both systems, the theoretical bounds on the communication rate are compared to the simulated rates. View Full-Text
Keywords: nonlinear systems; observers; data-rate constraints nonlinear systems; observers; data-rate constraints
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Voortman, Q.; Pogromsky, A.Y.; Matveev, A.S.; Nijmeijer, H. Data-Rate Constrained Observers of Nonlinear Systems. Entropy 2019, 21, 282.

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