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Data-Rate Constrained Observers of Nonlinear Systems.

Quentin Voortman¹, Alexander Yu Pogromsky^1,2, Alexey S Matveev^2,3

¹Department of Mechanical Engineering, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

This summary is machine-generated.

This study presents a robust observer for dynamical systems with limited data rates. It provides methods to calculate communication rate bounds, improving state estimation over noisy channels.

Keywords:

data-rate constraints nonlinear systems observers

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Area of Science:

Control Systems Engineering
Dynamical Systems Theory
Information Theory

Background:

State estimation in dynamical systems is crucial for remote monitoring and control.
Limited communication bandwidth poses a significant challenge for real-time state estimation.
Existing methods often lack robustness to communication channel losses.

Purpose of the Study:

To design a data-rate constrained observer for discrete and continuous-time dynamical systems.
To ensure the observer is robust to communication channel losses.
To establish theoretical bounds on the communication rates required for effective state estimation.

Main Methods:

Design of a discrete-time and continuous-time observer operating under data-rate constraints.
Development of robustness against communication channel losses.
Derivation of upper bounds on communication rates using state-space dimensions and system Jacobian properties.
Calculation of analytical minimum communication rate bounds using Lyapunov dimension.

Main Results:

The observer provides reliable state estimates despite communication channel losses.
Theoretical upper bounds on communication rates were derived using upper box dimension and system Jacobian.
Analytical bounds on the minimum required communication rate were established using Lyapunov dimension.
Simulations on the Lozi map and Lorenz system validated the theoretical bounds against actual rates.

Conclusions:

The proposed observer effectively estimates system states under data-rate constraints and channel losses.
Lyapunov dimension provides a tighter analytical bound for minimum communication rates compared to upper box dimension.
The findings offer practical guidelines for designing state estimation systems with limited communication capabilities.