NNs-observer-based fully distributed consensus control for MASs under deception attacks

•Unlike [7,8] and [31], which designs the controller under the assumption that the system states are available and the Lipschitz condition is needed for the nonlinear term. This paper designs the NNs-based observer to estimate unknown states and approximate nonlinear terms simultaneously, which guarantees the robustness and stability of the MASs can be improved.•Compared to Yang et al. [20], He et al. [21], Ma et al. [22], Liu et al. [23], Fu et al. [24], Zhao and Yang [25] dealing with deception attacks by using the global topology information, the fully distributed intrusion-tolerance control scheme is designed in this paper to achieve the consensus control for multi-agent systems that suffer from deception attacks, which only uses adjacent agent information in the design process of controller. In addition, the impact of the error signal injected by the attacker on the adaptive parameters are considered. This paper proposes a novel resilient intrusion-tolerance control scheme to solve the consensus control problem of multi-agent systems (MASs) under deception attacks. Consider the state unavailability of MASs with unknown nonlinear terms, the unmeasurable state is estimated by designing the neural-networks(NNs)-based observer. Then, a fully distributed intrusion-tolerant adaptive protocol is developed to implement the consensus control task. The designed control strategy only involves the agent states that interact with the neighboring agent and does not relate to the whole communication topology information. The designed controller can ensure that the consensus error of the nonlinear MASs is eventually ultimately bounded under deception attacks. Finally, a numerical simulation is provided to verify the feasibility of the designed scheme.