Adaptive Neural Network Boundary Security Consensus Control of Nonlinear Delayed Multiagent PDE Systems Under Hybrid Attacks.

This article considers the security consensus control problem for nonlinear delayed multiagent systems (MASs) modeled by partial differential equations (PDEs), which have unknown boundary nonlinearities and are subjected to hybrid attacks including deception and denial-of-service (DoS) attacks. To address these challenges, a composite adaptive neural network boundary security consensus controller is proposed, which consists of a boundary security consensus control component that guarantees the achievement of security consensus control in the mean square under hybrid attacks and an adaptive component that approximates the unknown boundary nonlinearities via a neural network with an adaptive weight update law. Afterward, Lyapunov-based analysis and linear matrix inequality (LMI) techniques are combined to derive sufficient conditions for the nonlinear delayed error system to be practically exponentially stable (PES) in the mean square, under unknown boundary nonlinearities and hybrid attacks. Finally, numerical simulations validate the effectiveness of the proposed control strategy for nonlinear delayed multiagent PDE systems with one leader agent and four follower agents under unknown boundary nonlinearities and hybrid attacks.