Optimal Output Feedback Control Using Two Remote Sensors Over Erasure Channels

Abstract

ISR develops, applies and teaches advanced methodologies of design and analysis toIf an erasure event occurs, then any information conveyed over the link is lost. This paper addresses the problem of designing the maps that specify the processing at the controller and at the sensors to minimize a quadratic cost function. When the information is lost over the links either in an independent and identically distributed (i.i.d.) or (time-homogeneous) Markovian fashion, we derive necessary and sufficient conditions for the existence of maps such that the plant is stabilized in the bounded second moment sense. We also solve the optimal design problem in the presence of delayed noiseless acknowledgment signals at the sensors from the controller for any arbitrary packet drop pattern. We provide explicit recursive schemes to implement our solution. We also indicate how our approach can be extended to situations when more than two sensors are available, when the sensors can cooperate and when the acknowledgment link features erasure. The analysis also carries over to the case when each point-to-point erasure link connecting the sensors and the controller is replaced by a network of erasure links.

On Kalman Filtering with Fading Wireless Channels Governed by Power Control

“…Representative works include Sinopoli et al (2004); Xie and Xie (2008); Schenato (2008); Kluge et al (2010); Gupta et al (2009);Shi et al (2010); Dey et al (2009). However, to the best of the authors' knowledge, such kind of stability analysis has not been performed previously for the case of state estimation with power controlled digital wireless links.…”

On stability in the presence of analog erasure channels

“…Both the above two theorems can be proven in a similar fashion as the centralized case by using the results from [12]. We omit the proof here.…”

“…Note that if either the assumption B or assumption C holds and, moreover, if each individual controller has access to data transmitted by every other controller, the problem reduces to the cases considered by [12], [4]. While interesting first steps, the problem formulation in those works is not truly distributed.…”

“…fashion, while Gupta et al [8] considered multiple sensors and more general erasure models. Recent research has also addressed the case where multiple sensors and erasure channels are present [12], [4], although we would like to argue that the V. Gupta is with the Department of Electrical Engineering, University of Notre Dame. Email: vgupta2@nd.edu N. C. Martins is with the Institute for Systems Research, University of Maryland, College Park.…”

“…This view was taken, e.g., in [10], [9], [12], [5]. This pre-processing strategy can also be seen in the recent results on receding horizon networked control, in which a few future control inputs are transmitted at every time step by the controller and buffered at the actuator to be used in case subsequent control updates are dropped by the network and do not arrive at the actuator(s) [6], [7], [16], [19], [20].…”