Summary: This study addresses an event-triggered distributed \(\mathscr{H}_\infty\) control method by extending traditional zero-sum differential games for physically interconnected non-holonomic mobile mechanical multi-agent systems with external disturbance and slipping, skidding and dead-zone disturbances. Initially, a problem of physically interconnected kinematic and dynamic control is transformed into an equivalent problem of event-triggered distributed \(\mathscr{H}_\infty\) control. Subsequently, the traditional two-player zero-sum differential game is extended to a three-player zero-sum differential game, where a new player is included to approximate the worst dead-zone disturbance. To find player policies, an event-triggering condition and an event-triggered control law are proposed via neural networks (NNs). Although an NN weight-tuning law is designed on the basis of adaptive dynamic programming techniques, it can relax identification procedures for unknown drift dynamics and persistent excitation conditions. It also guarantees that the closed system is stable and the cost function converges to the bounded \(\mathscr{L}_2\)-gain optimal value, while the Zeno behaviour is excluded. Finally, the effectiveness of the proposed method is verified by an application to a dead-zone torque multi-mobile robot system through numerical simulations.
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