TY - JOUR

T1 - Observation of nonlinear systems via finite capacity channels, Part II

T2 - Restoration entropy and its estimates

AU - Matveev, Alexey S.

AU - Pogromsky, Alexander Yu

PY - 2019/5

Y1 - 2019/5

N2 - The paper deals with the state estimation problem for nonlinear dynamical systems via communication channels with limited data rate. We introduce several minimum data-rate limits associated with various types of observability. A notion of the restoration entropy (RE) is also introduced and its relevance to the problem is outlined by a corresponding Data Rate Theorem. Theoretical lower and upper estimates for the RE are proposed in the spirit of the first and second Lyapunov methods, respectively. For three classic chaotic multi-dimensional systems, it is demonstrated that the lower and upper estimates for the RE coincide for one of them and are nearly the same for the others.

AB - The paper deals with the state estimation problem for nonlinear dynamical systems via communication channels with limited data rate. We introduce several minimum data-rate limits associated with various types of observability. A notion of the restoration entropy (RE) is also introduced and its relevance to the problem is outlined by a corresponding Data Rate Theorem. Theoretical lower and upper estimates for the RE are proposed in the spirit of the first and second Lyapunov methods, respectively. For three classic chaotic multi-dimensional systems, it is demonstrated that the lower and upper estimates for the RE coincide for one of them and are nearly the same for the others.

KW - Entropy

KW - Lyapunov function

KW - Nonlinear systems

KW - Observability

KW - Reliable state estimation

UR - http://www.scopus.com/inward/record.url?scp=85060164325&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2019.01.019

DO - 10.1016/j.automatica.2019.01.019

M3 - Article

AN - SCOPUS:85060164325

VL - 103

SP - 189

EP - 199

JO - Automatica

JF - Automatica

SN - 0005-1098

ER -