TY - GEN

T1 - Entropy notions for state estimation and model detection with finite-data-rate measurements

AU - Liberzon, Daniel

AU - Mitra, Sayan

PY - 2016/12/27

Y1 - 2016/12/27

N2 - We study a notion of estimation entropy for continuous-time nonlinear systems, formulated in terms of the number of system trajectories that approximate all other trajectories up to an exponentially decaying error. We also consider an alternative definition of estimation entropy which uses approximating functions that are not necessarily trajectories of the system, and show that the two entropy notions are equivalent. We establish an upper bound on the estimation entropy in terms of the sum of the desired convergence rate and an upper bound on the matrix measure of the Jacobian, multiplied by the system dimension. We describe an iterative procedure that uses quantized and sampled state measurements to generate state estimates that converge to the true state at the desired exponential rate. The average bit rate utilized by this procedure matches the derived upper bound on the estimation entropy. We also show that no other algorithm of this type can perform the same estimation task with bit rates lower than the estimation entropy. Finally, we discuss an application of the estimation procedure in determining, from the quantized state measurements, which of two competing models of a dynamical system is the true model. We show that under a mild assumption of exponential separation of the candidate models, detection always happens in finite time.

AB - We study a notion of estimation entropy for continuous-time nonlinear systems, formulated in terms of the number of system trajectories that approximate all other trajectories up to an exponentially decaying error. We also consider an alternative definition of estimation entropy which uses approximating functions that are not necessarily trajectories of the system, and show that the two entropy notions are equivalent. We establish an upper bound on the estimation entropy in terms of the sum of the desired convergence rate and an upper bound on the matrix measure of the Jacobian, multiplied by the system dimension. We describe an iterative procedure that uses quantized and sampled state measurements to generate state estimates that converge to the true state at the desired exponential rate. The average bit rate utilized by this procedure matches the derived upper bound on the estimation entropy. We also show that no other algorithm of this type can perform the same estimation task with bit rates lower than the estimation entropy. Finally, we discuss an application of the estimation procedure in determining, from the quantized state measurements, which of two competing models of a dynamical system is the true model. We show that under a mild assumption of exponential separation of the candidate models, detection always happens in finite time.

UR - http://www.scopus.com/inward/record.url?scp=85010781170&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010781170&partnerID=8YFLogxK

U2 - 10.1109/CDC.2016.7799402

DO - 10.1109/CDC.2016.7799402

M3 - Conference contribution

AN - SCOPUS:85010781170

T3 - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

SP - 7335

EP - 7340

BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 55th IEEE Conference on Decision and Control, CDC 2016

Y2 - 12 December 2016 through 14 December 2016

ER -