TY - GEN
T1 - Topological entropy of switched nonlinear systems
AU - Yang, Guosong
AU - Liberzon, Daniel
AU - Hespanha, João P.
N1 - Funding Information:
G. Yang and J. P. Hespanha’s work was supported by the Office of Naval Research MURI grant N00014-16-1-2710, and by the National Science Foundation grant EPCN-1608880. D. Liberzon’s work was supported by the National Science Foundation grant CMMI-1662708, and by the Air Force Office of Scientific Research grant FA9550-17-1-0236.
Publisher Copyright:
© 2021 Owner/Author.
PY - 2021/5/19
Y1 - 2021/5/19
N2 - This paper studies topological entropy of switched nonlinear systems. We construct a general upper bound for the topological entropy in terms of an average of the asymptotic suprema of the measures of Jacobian matrices of individual modes, weighted by the corresponding active rates. A general lower bound is constructed in terms of an active-rate-weighted average of the asymptotic infima of the traces of these Jacobian matrices. For switched systems with diagonal modes, we construct upper and lower bounds that only depend on the eigenvalues of Jacobian matrices, their relative order among individual modes, and the active rates. For both cases, we also construct more conservative upper bounds that require less information on the switching, with their relations illustrated by numerical examples of a switched Lotka-Volterra ecosystem model.
AB - This paper studies topological entropy of switched nonlinear systems. We construct a general upper bound for the topological entropy in terms of an average of the asymptotic suprema of the measures of Jacobian matrices of individual modes, weighted by the corresponding active rates. A general lower bound is constructed in terms of an active-rate-weighted average of the asymptotic infima of the traces of these Jacobian matrices. For switched systems with diagonal modes, we construct upper and lower bounds that only depend on the eigenvalues of Jacobian matrices, their relative order among individual modes, and the active rates. For both cases, we also construct more conservative upper bounds that require less information on the switching, with their relations illustrated by numerical examples of a switched Lotka-Volterra ecosystem model.
KW - nonlinear systems
KW - switched systems
KW - topological entropy
UR - http://www.scopus.com/inward/record.url?scp=85105862283&partnerID=8YFLogxK
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U2 - 10.1145/3447928.3456642
DO - 10.1145/3447928.3456642
M3 - Conference contribution
AN - SCOPUS:85105862283
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, Inc
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 -