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In this study,we consider the generation of optimal persistent formations for heterogeneous multi-agent systems,with the leader constraint that only specific agents can act as leaders.We analyze three modes to control the optimal persistent formations in two-dimensional space,thereby establishing a model for their constrained generation.Then,we propose an algorithm for generating the optimal persistent formation for heterogeneous multi-agent systems with a leader constraint (LC-HMAS-OPFGA),which is the exact solution algorithm of the model,and we theoretically prove its validity.This algorithm includes two keel sub-algorithms,which are optimal persistent graph generating algorithm based on a minimum cost arborescence and the shortest path (MCA-SP-OPGGA),and the optimal persistent graph adjusting algorithm based on the shortest path (SP-OPGAA).Under a given agent formation shape and leader constraint,LC-HMAS-OPFGA first generates the network topology and its optimal rigid graph corresponding to this formation shape.Then,LC-HMAS-OPFGA uses MCA-SP-OPGGA to direct the optimal rigid graph to generate the optimal persistent graph.Finally,LC-HMAS-OPFGA uses SP-OPGAA to adjust the optimal persistent graph until it satisfies the leader constraint.We also demonstrate the algorithm,LC-HMAS-OPFGA,with an example and verify its effectiveness.