TY - JOUR

T1 - Optimal capacity allocation for sampled networked systems

AU - Chen, Xudong

AU - Belabbas, Mohamed Ali

AU - Başar, Tamer

N1 - Funding Information:
Research of T. Ba?ar was supported in part by the U.S. Air Force Office of Scientific Research (AFOSR) MURI grant FA9550-10-1-0573 and in part by National Science Foundation (NSF) grant CCF 11-11342; Research of M.-A. Belabbas was supported in part by National Science Foundation (NSF)ECCS 13-07791 and in part by National Science Foundation (NSF)ECCS CAREER 13-51586. The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Tongwen Chen under the direction of Editor Ian R. Petersen.

PY - 2017/11

Y1 - 2017/11

N2 - We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements. We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the estimation is bounded above, and that each sample requires the same amount of communication. Our goal is then to find an optimal allocation of the capacity to the sensors so that the time-averaged estimation error is minimized. We show that when the total available channel capacity is large, this resource allocation problem can be recast as a strictly convex optimization problem, and hence there exists a unique optimal allocation of the capacity. We further investigate how this optimal allocation varies as the available capacity increases. In particular, we show that if the coupling among the subsystems is weak, then the sampling rate allocated to each sensor is nondecreasing in the total sampling rate, and is strictly increasing if and only if the total sampling rate exceeds a certain threshold.

AB - We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements. We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the estimation is bounded above, and that each sample requires the same amount of communication. Our goal is then to find an optimal allocation of the capacity to the sensors so that the time-averaged estimation error is minimized. We show that when the total available channel capacity is large, this resource allocation problem can be recast as a strictly convex optimization problem, and hence there exists a unique optimal allocation of the capacity. We further investigate how this optimal allocation varies as the available capacity increases. In particular, we show that if the coupling among the subsystems is weak, then the sampling rate allocated to each sensor is nondecreasing in the total sampling rate, and is strictly increasing if and only if the total sampling rate exceeds a certain threshold.

KW - Algebraic Riccati equations

KW - Capacity filtration

KW - Mean squared error estimation

KW - Optimal capacity allocation

KW - Sampled networked systems

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U2 - 10.1016/j.automatica.2017.07.039

DO - 10.1016/j.automatica.2017.07.039

M3 - Article

AN - SCOPUS:85027553146

VL - 85

SP - 100

EP - 112

JO - Automatica

JF - Automatica

SN - 0005-1098

ER -