Fixed-time event-triggered and periodic event-triggered containment control for heterogeneous multi-agent systems under DoS attacks

This study explores the fixed-time containment control problem for heterogeneous multi-agent systems (HMASs) under denial-of-service (DoS) attacks. A continuous control scheme is provided to enable HMASs to solve fixed-time containment control problems with unknown DoS attacks and arbitrary initial conditions. To reduce the frequency of controller updates, a novel control strategy based on event-triggered conditions has been designed, which can settle the fixed-time containment control issue without requiring continuous controller updates. In the scenario where the initial states of the systems are bound, an improved event-triggered control scheme with periodic event-triggered conditions is designed, which can avoid continuous controller updates and does not need continuous system messages. Compared with many existing results, all the designed control schemes can settle fixed-time containment issues even when the DoS attacks and initial conditions are unknown. Moreover, the given event-based control schemes can avoid Zeno-behavior. Numerical examples are provided to support the results.