Event-triggered concurrent-learning optimal containment control for discrete-time multi-agent systems

This paper studies distributed optimal containment control for linear discrete-time multi-agent systems with multiple autonomous leaders. An event-triggered concurrent-learning (ET-CL) adaptive dynamic programming framework is developed. It reduces communication and retains informative transient data after online excitation decays. The containment task is reformulated as stabilization of coupled local errors. A stacked linear-quadratic game supplies a verifiable Nash benchmark. The distributed actor realizes a local projection of this benchmark. The omitted coupling is treated as a bounded approximation residual. Coupled discrete-time algebraic Riccati equations and rank-robustness conditions for sampled history stacks are provided. A closed-loop bound on state increments is also derived. Under the stated rank, state-span and admissible-initialization conditions, the critic and actor weight errors and the containment errors are uniformly ultimately bounded. A three-follower study verifies the Riccati residual and closed-loop Schur margin. It also tests the learned controller under the considered follower-side perturbations of S and B i .