Control Over Wireless Communication Channel for Continuous-Time Systems

This paper is concerned with the control of one dimensional continuous time linear Gaussian systems over additive white noise wireless fading channels subject to capacity constraints. Necessary and sufficient conditions are derived, for bounded asymptotic and asymptotic observability and stabilizability in the mean square sense, for controlling such systems. For the case of a noiseless time-invariant system controlled over a continuous time additive white Gaussian channel, the sufficient condition for stabilizability and observability states that the capacity of the channel, C
a
, satisfies, C
a
> [A]
⁺
, where A is the system coefficient and [a]
⁺
= a, if a ≥0 and [a]
⁺
= 0, if a < 0. Moreover, the necessary condition states that the channel capacity must satisfy C
a
≥ [A]
⁺
. It is shown that a separation principle holds between the design of the communication and the control sub-systems, implying that the controller that would be optimal in the absence of the communication channel is also optimal for the problem of the controlling the system over the communication channel.