Prescribed performance secure synchronization for nonlinear heterogeneous multi-agent systems under multiple attacks

In this paper, the prescribed performance secure synchronization problem is investigated for nonlinear heterogeneous multi-agent systems under multiple attacks. First, an error transformation is ingeniously constructed by combining the local neighborhood error affected by attacks with a novel performance function that can flexibly adjust boundaries. Second, a triggering mechanism with the dynamically tunable threshold is designed, and based on radial basis function neural networks, a state feedback secure control protocol without continuous information transmission is proposed under the condition that all system states are measurable. Further, in the context of only system outputs are measurable, an observer-based event-triggered output feedback secure control protocol is devised, which ensures that the output synchronization error and all closed-loop system signals still converge to an adjustable bounded neighborhood. Particularly, the internal dynamic variable embedded within the triggering mechanism plays a pivotal role in prolonging triggering intervals, thereby enabling the proposed control protocols to resist both sensor and actuator attacks in an energy-conserving manner while ensuring that the local neighborhood error satisfies prescribed performance demands. Ultimately, the examples are employed to validate the effectiveness of control schemes.