On a connection between the reliability of multi-channel systems and the notion of controlled-invariance entropy

Abstract

The purpose of this note is to establish a connection between the problem of reliability (when there is an intermittent control-input channel failure that may occur between actuators, controllers and/or sensors in the system) and the notion of controlled-invariance entropy of a multi-channel system (with respect to a subset of control-input channels and/or a class of control functions). We remark that such a connection could be used for assessing the reliability (or the vulnerability) of the system, when some of these control-input channels are compromised with an external "malicious" agent that may try to prevent the system from achieving more of its goal (such as from attaining invariance of a given compact state and/or output subspace).