This analysis presents a distributed optimal control policy for consensus in multi-agent systems, indicating the method achieves a global Nash equilibrium.
This paper studies the graphical game for multi‐agent systems with Lipschitz nonlinear dynamics over directed graphs. First, a distributed optimal control policy is presented to ensure the leader‐following consensus. Then, a modified cost function in the framework of graphical games is designed such that the weighting matrix is time‐varying and relies on the Lipschitz nonlinearity, leading to the global Nash equilibrium. A simulation study is finally provided.
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Zhang et al. (2025) studied this question.
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