Resilient abstraction-based hierarchical control of linear systems

Abstract

This paper develops a resilient hierarchical control structure for cyber–physical systems (CPSs) using an extended resilient approximate simulation function. Data transmission through wireless communication channels in CPSs is vulnerable to cyber-attacks. Furthermore, these systems may be modeled using linear dynamics with high-state dimensions. Hence, the control synthesis problem for concrete systems is computationally challenging. The extended resilient approximate simulation function introduced in this paper enables the use of an abstract system for computationally efficient controller design. This function is mathematically defined as the sum of the resilient approximate simulation function between the abstract model and the unknown input observer (UIO), and the simple approximate simulation function between the UIO and the concrete system. Accordingly, the controller can first be designed for the abstract system and then refined for the concrete system by introducing an appropriate interface controller. This controller constitutes an observer-based robust control law based on $H_{\infty }$ to guarantee the desired performance despite external disturbances and includes an adaptive compensator to mitigate the effect of attacks on the simulation relation. The applicability of the presented approach is demonstrated through two case studies: load frequency control in a power system and frequency regulation in an isolated area of the New England 39-Bus Test System.