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We investigate the pullback asymptotic compactness of solution operators and the asymptotically autonomous robustness of pullback attractors for a non-autonomous Yukawa coupling Klein–Gordon–Schrödinger (KGS) equations defined on an unbounded domain   $\mathbb{R}^{d}$   with   $1\leqslant d\leqslant 3$  . Under some new high-order integrability conditions found in this paper on the time-dependent external forces, we demonstrate that the non-autonomous dynamical system associated with the solution operator admits a unique pullback attractor   $\{\mathfrak{A}(\tau )\}_{\tau \in \mathbb{R}}$   in   $\mathbb{H}:= H^{1}(\mathbb{R}^{d})\times H^{1}(\mathbb{R}^{d})\times L^{2}(\mathbb{R}^{d})$  . When the time-dependent external forces converge to given time-independent functions, we prove that the time-component   $\mathfrak{A}(\tau )$   converges to the global attractor (obtained by Guo and Li [21], and Lu and Wang [38]) of the autonomous KGS equation as   $\tau $   tends to positive and negative infinity, respectively. Unlike the methods of Caraballo  et al.  [14], Kinra  et al.  [26], and Wang  et al.  [58], we give up using the uniform pullback asymptotic compactness of the solution operators over the infinite time-intervals   $[\tau ,+\infty )$   and   $(-\infty ,\tau ]$  . The famous idea of energy equations due to Ball [6] and method of uniform tail-ends estimates of Wang [52], originally used in the autonomous case, are adapted in the nonautonomous case in order to derive the pullback asymptotic compactness of the solution operators in   $\mathbb{H}$  , where the difficulties caused by the non-compactness of Sobolev embeddings on   $\mathbb{R}^{d}$   and the weak dissipativeness of the KGS equations are surmounted.

Pullback Asymptotic Compactness and Asymptotically Autonomous Robustness of Non-autonomous Klein–Gordon–Schrödinger System on Unbounded Domains