Outer synchronization in drive-response cyber-physical systems with time-varying delays via adaptive control

In this paper, a cyber-physical system under attack is modeled by a descriptor system with unknown inputs. By partitioning the descriptor system into several disjoint areas, we build a drive-response descriptor system and discuss the adaptive control problem in different situations based on Lyapunov stability theory. First, parameter update laws are presented to identify the unknown system parameters. Second, adaptive controllers are designed to deal with the problem of outer synchronization between the drive system and the response system. Third, it is proved that the effects of unknown inputs and time-varying delays are compensated by the adaptive controllers. Finally, several numerical simulations are carried out to illustrate the effectiveness of the update laws and adaptive controllers.