TY - GEN
T1 - Quantizer design for switched linear systems with minimal data-rate
AU - Vicinansa, Guilherme S.
AU - Liberzon, Daniel
N1 - Publisher Copyright:
© 2021 ACM.
PY - 2021/5/19
Y1 - 2021/5/19
N2 - In this paper, we present a quantization scheme that reconstructs the state of switched linear systems with a prescribed exponential decaying rate for the state estimation error. We show how to use the Lyapunov exponents and a geometric object called Oseledets' filtration to design such a quantization scheme. Then, we prove that this algorithm works at an average data-rate close to the estimation entropy of the given system. Furthermore, we can choose the average data-rate to be arbitrarily close to the estimation entropy whenever the switched linear system has the so-called regularity property. We show that, under the regularity assumption, the quantization scheme is completely causal in the sense that it only depends on information that is available at the current time instant. Finally, we present simulation results for a Markov Jump Linear System, a class of systems for which the realizations are known to be regular with probability 1.
AB - In this paper, we present a quantization scheme that reconstructs the state of switched linear systems with a prescribed exponential decaying rate for the state estimation error. We show how to use the Lyapunov exponents and a geometric object called Oseledets' filtration to design such a quantization scheme. Then, we prove that this algorithm works at an average data-rate close to the estimation entropy of the given system. Furthermore, we can choose the average data-rate to be arbitrarily close to the estimation entropy whenever the switched linear system has the so-called regularity property. We show that, under the regularity assumption, the quantization scheme is completely causal in the sense that it only depends on information that is available at the current time instant. Finally, we present simulation results for a Markov Jump Linear System, a class of systems for which the realizations are known to be regular with probability 1.
KW - estimation entropy
KW - quantizer design
KW - switched systems
UR - http://www.scopus.com/inward/record.url?scp=85105870642&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85105870642&partnerID=8YFLogxK
U2 - 10.1145/3447928.3456645
DO - 10.1145/3447928.3456645
M3 - Conference contribution
AN - SCOPUS:85105870642
T3 - HSCC 2021 - Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control (part of CPS-IoT Week)
BT - HSCC 2021 - Proceedings of the 24th International Conference on Hybrid Systems
PB - Association for Computing Machinery
T2 - 24th ACM International Conference on Hybrid Systems Computation and Control, HSCC 2021, held as part of the 14th Cyber Physical Systems and Internet-of-Things Week, CPS-IoT Week 2021
Y2 - 19 May 2021 through 21 May 2021
ER -