TY - JOUR
T1 - Minimax estimation with intermittent observations
AU - Moon, Jun
AU - Başar, Tamer
N1 - Funding Information:
This research was supported in part by the US Air Force Office of Scientific Research (AFOSR) MURI grant FA9550-10-1-0573 . The material in this paper was partially presented at the 52nd IEEE Conference on Decision and Control, December 10–13, 2013, Florence, Italy. This paper was recommended for publication in revised form by Associate Editor Tongwen Chen under the direction of Editor Ian R. Petersen.
Publisher Copyright:
© 2015 Elsevier Ltd.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015/12
Y1 - 2015/12
N2 - This paper considers a problem of minimax (or H∞) state estimation with intermittent observations. In this setting, the disturbance in the dynamical system and the sensor noise are controlled by adversaries, and the estimator receives the sensor measurements only sporadically, with the availability governed by an independent and identically distributed Bernoulli process. We cast this problem within the framework of stochastic zero-sum dynamic games. We first obtain a corresponding stochastic minimax state estimator (SMSE) and an associated generalized stochastic Riccati equation (GSRE) whose evolutions depend on two parameters: one that governs the random measurement arrivals and another one that quantifies the level of H∞ disturbance attenuation. We then analyze the asymptotic behavior of the sequence generated by the GSRE in the expectation sense, and its weak convergence. Specifically, we obtain threshold-type conditions above which the sequence generated by the GSRE can be bounded both below and above in the expectation sense. Moreover, we show that under some conditions, the norm of the sequence generated by the GSRE converges weakly to a unique stationary distribution. Finally, we prove that when the disturbance attenuation parameter goes to infinity, our asymptotic results are equivalent to the corresponding results from the literature on Kalman filtering with intermittent observations. We provide simulations to illustrate the results.
AB - This paper considers a problem of minimax (or H∞) state estimation with intermittent observations. In this setting, the disturbance in the dynamical system and the sensor noise are controlled by adversaries, and the estimator receives the sensor measurements only sporadically, with the availability governed by an independent and identically distributed Bernoulli process. We cast this problem within the framework of stochastic zero-sum dynamic games. We first obtain a corresponding stochastic minimax state estimator (SMSE) and an associated generalized stochastic Riccati equation (GSRE) whose evolutions depend on two parameters: one that governs the random measurement arrivals and another one that quantifies the level of H∞ disturbance attenuation. We then analyze the asymptotic behavior of the sequence generated by the GSRE in the expectation sense, and its weak convergence. Specifically, we obtain threshold-type conditions above which the sequence generated by the GSRE can be bounded both below and above in the expectation sense. Moreover, we show that under some conditions, the norm of the sequence generated by the GSRE converges weakly to a unique stationary distribution. Finally, we prove that when the disturbance attenuation parameter goes to infinity, our asymptotic results are equivalent to the corresponding results from the literature on Kalman filtering with intermittent observations. We provide simulations to illustrate the results.
KW - Intermittent observations
KW - Kalman filtering
KW - Minimax estimation ( estimation)
KW - Networked control systems
KW - Zero-sum dynamic games
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U2 - 10.1016/j.automatica.2015.09.004
DO - 10.1016/j.automatica.2015.09.004
M3 - Article
AN - SCOPUS:84947709651
SN - 0005-1098
VL - 62
SP - 122
EP - 133
JO - Automatica
JF - Automatica
ER -