Controllability of autonomous decentralized systems

This paper proposes a new definition of controllability for autonomous decentralized systems (ADSs). This controllability is defined as controllability of the entire system in spite of failures in some subsystems. The degree of fault-tolerance is measured with the number of its allowed faulty subsystems. A necessary and sufficient condition for the controllability and its basic properties are shown. To satisfy the requirement for expansibility for ADSs, the homogeneity and symmetry are favorable. However, this paper clarifies that symmetric systems are uncontrollable. Certain failures in some subsystems cause the system to be symmetric and uncontrollable. Therefore it should be noted the tight relationships between the symmetry of systems and the autonomous controllability. The homogeneity and symmetry originated from the expansibility have some aspects that do not consist fault-tolerance.<>