The consensus problem under a single leader forms the foundation of coordination control in multi-agent systems (MASs). Nonetheless, the issue of containment control, which involves multiple leaders, represents a critical aspect that demands further investigation. This paper addresses the containment control of nonlinear heterogeneous partial difference multi-agent systems (HPDMASs) characterized by state time delays and governed by hyperbolic or parabolic partial difference equations. This study proposes a D-type distributed iterative containment control protocol incorporating initial state learning, which leverages local state information from neighboring agents. Using the contraction mapping principle, this research examines the convergence conditions for the containment error within a finite time interval. The results demonstrate that, under the proposed containment control protocol, the containment error in the HPDMASs can gradually converge to zero as the number of iterations increases. Simulation results are provided to validate the effectiveness of the proposed control protocol.
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