Distributed fixed-time Nash equilibrium seeking algorithm for multiple ASVs: A hybrid event-triggered approach

Fixed‐time consensus of networked Euler–Lagrange systems over event‐based communication under DoS attacks

“…The variables $$$ \sum \limits_{j=1}^n{a}_{ij}{\left\Vert {x}_i\left({t}_i^k\right)-{x}_j\left({t}_j^k\right)\right\Vert}^2 $$$ and $$$ {\omega}_{i2} $$$ respectively are state‐based threshold and internal dynamic variable, and used to reduce the number of communication triggers. In particular, the dynamic variable $$$ {\omega}_{i2} $$$ is designed to match with the fixed‐time stability while eliminating Zeno behavior 43 . Besides, arising the gains $$$ {r}_3 $$$ and $$$ {r}_4 $$$ may contribute to minimize the number of triggers, but it has a negative impact on system performance.…”