On the theory of estimation and control with finite data-rate

In this dissertation, we discuss control and estimation problems for systems that operate with data-rate constraints. We start by studying the estimation entropy of switched linear systems. This quantity is the minimal data-rate we need to use to estimate the state of a switched linear system with an estimation error that decays with a prescribed exponential decay rate. We provide upper and lower bounds for the estimation entropy in terms of the Lyapunov exponents of the switched system. Also, we show that those bounds coincide with the entropy when the system is Lyapunov regular. We provide a coding scheme that solves the state reconstruction problem with the data rate as close as desired to the minimum. Under the regularity assumption, we show how to make that algorithm work causally. Next, we present sufficient conditions for a system to be Lyapunov regular and show that Markov Jump Linear Systems belong to that class. We also illustrate those theoretical results with simulations. Then, we switch subjects to the problem of defining controllability for linear time-varying systems with a finite data-rate. We explain why the usual notion of controllability is unfit when data-rate constraints are present. Then, we define a new controllability notion that makes sense in this scenario. We also justify why such a notion is natural. Next, we present a necessary condition and a sufficient condition for a system to be controllable with a finite data-rate. Finally, we revisit the topic of controllability with a finite data-rate, but we specialize our analysis to switched linear systems. Although this part of the work is more restrictive than the previous one, we show how the switched system structure allows us to derive sufficient conditions for our system to be controllable with a finite data-rate using information about the individual modes and some mild assumptions about the switching signal. In particular, when our switching signal satisfies an average dwell-time condition, we give a simple relation between the sampling time, chatter bound, and average-dwell time that guarantees that our system will be controllable with a finite data-rate. Then, we generalize our analysis by assuming we can have packet losses in our communication channel. We prove a sufficient condition for such a system to be controllable with a finite data-rate even when we might lose packets. We demonstrate this condition by constructing an algorithm, which makes this proof constructive.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Scabin Vicinansa, Guilherme

Contributors dc:contributor

• Liberzon, Daniel
• Belabbas, Mohammed-Ali
• Baryshnikov, Yuliy
• Zharnitsky, Vadim

• Estimation Entropy
• Finite Data-rate

Statement dc:rights

• Copyright 2023 Guilherme Scabin Vicinansa

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/121350

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F121350