Threshold-Dependent Secure Event-Triggered Control for Networked Systems Under Denial of Service Attacks

Event-triggered control addresses a communication resource constraint challenge for networked control systems (NCS) but it is vulnerable to denial of service (DoS) attacks. This paper is concerned with the secure event-triggered control problem for NCSs under DoS attacks. The novelty lies in the development of a novel threshold-dependent event-triggered transmission scheme and a co-design approach for the event-triggered scheme and the desired secure controller. First, two threshold concepts, namely the critical event-triggered threshold (CETT) and the secure event-triggered threshold (SETT), are proposed for the event-triggered scheme. More specifically, the CETT is defined by the maximum allowable event-triggered parameter which can guarantee stability of the NCS and the SETT is used to ensure timely transmissions when the NCS subject to DoS-resulted packet dropouts. Second, by virtue of the input delay approach, a comprehensive closed-loop system model is derived for the NCS, which accommodates simultaneously the event-based sporadic transmissions, packet delays, and DoS-resulted packet dropouts. Third, a co-design algorithm is presented to determine both the desired threshold parameter and secure state- and output-feedback secure controllers. Finally, numerical simulations on a CAN-based vehicle lateral control system are provided to demonstrate the efficacy of the proposed control method. Note to Practitioners—This paper was motivated by the secure control design problem of the NCSs subject to both limited communication resources and DoS attacks. Most existing works failed to establish the relation between event-triggered parameter and packet dropouts and thus lead to the difficulties in controller synthesis under DoS attacks. In this paper, we mathematically characterize the relation between event-triggered parameter and the number of DoS-resulted packet dropouts. The secure control and event-triggered communication co-design approach of the networked control systems under malicious attacks is carefully derived. To practitioners, this study provides a secure control design basis of the NCS subject to DoS attacks by analyzing the evolution of event-triggered threshold under DoS-resulted packet dropouts. However, such design method just mitigates the effects caused by DoS attacks but is less of ability to regulate the control actions during DoS attack intervals. In future research, the active and intelligent secure control compensation strategies will be addressed.