Adaptive containment control of nonlinear multi‐agent systems about privacy preservation with multiple attacks

Abstract

Summary This paper focuses on the problem of adaptive containment control about privacy preservation in nonlinear multi‐agent systems, where followers suffer from multiple cyber‐attacks and leaders have non‐zero control inputs. A multiple attacks mold consisting of denial‐of‐service (DoS) attacks and false data‐injection attacks is constructed for nonlinear systems. The containment control protocol is updated by applying an event‐triggered scheme. This scheme is proposed to dispatch the updating information in the presence of multiple attacks. Meanwhile, to deal with the information insecurity that may exist in the control process, the protocol for privacy preservation about initial information is developed by introducing time‐varying functions as masks. Tracking errors of agents are described by taking the inputs of leaders as the external disturbances. This method does not depend on the widths of boundary layers and reduce the computational complexity. The stability of multi‐agent systems is analyzed by applying the Cauchy inequality, the Young's inequality and the Lyapunov function theory. Finally, two simulation examples are shown to illustrate the effectiveness of the proposed control strategy.

A distributed containment tracking control of the UAV formation with prescribed performance subject to collision avoidance

“…Theorem 1. For UAV formation (2), the prescribed performance function is chosen as (10) and (11), the error transformation function is presented in (13), and the distributed finite-time containment tracking control inputs u f i and u f j are designed in (26) and (28). Given a positive constant 𝛾, if there exist matrices K L , K F and positive definite matrices P, Q, which satisfies…”

“…Lemma 1 (28). From Assumption 1, all eigenvalues of L 11 and L 22 have positive real parts, and each entry of −L −1 22 L 21 is nonnegative.…”

Secure group consensus of nonlinear multi‐agent systems with multiple attacks under periodic event‐triggered control

“…To be specific, the proposed controller (9) is updated at a lower frequency than those in References 16–18. On the other hand, mechanism (10) allows the triggering instant to occur at the sampling instant, which overcomes the uninterrupted judgment of triggering conditions in References 26,27 and avoids the Zeno behavior naturally.…”

“…Fortunately, the development of event‐triggered control (ETC) provides a direction to solve the problem, 24,25 that is, sampling actions are taken when the triggering function exceeds a certain threshold. Under the appropriate ETC strategies, the single and multiple attacks were handled respectively in References 26 and 27,28 for nonlinear MASs, however, the above work needs to monitor the triggering function in real time and proves that no Zeno behavior occurs. Notably, the periodic event‐triggered (PET) control combines the advantages of sampled‐data control and ETC, which periodically detects the triggering function at sampling instants, thereby avoiding Zeno behavior in nature 29 .…”

“…In particular, the designed compensator successfully realizes intermittent communication, which is superior to the continuous compensator in References 6,7,17 in terms of saving communication bandwidth resources. A PET output feedback control protocol is designed by compensator states, which is more suitable for practical applications than the state feedback control protocol in Reference 36 that requires all states to be measurable. Notably, distinct from the control protocol in References 26,27, the proposed PET control protocol contributes to intermittent monitoring of triggering function and natural avoidance of Zeno behavior. Using the GC technique, the secure group consensus is investigated for nonlinear MASs with multiple attacks, which is more challenging in control design and stability analysis compared with the work in References 30–32. Particularly, the GC technique simplifies the design process greatly by eliminating the stepwise iteration in References 12,13 and avoiding the solution of linear matrix inequalities in Reference 36.…”