Optimal Synchronization of Heterogeneous Multi-agent Systems with additional antagonistic input in Graphical Games

This paper investigates optimal synchronization control for heterogeneous linear multi-agent systems (MASs) under cooperative inputs and adversarial disturbances. A graphical game formulation reveals that Nash equilibrium strategies solving coupled Hamilton-Jacobi-Isaacs (HJI) equations achieve simultaneous synchronization and performance optimization while providing optimal disturbance rejection. To overcome the computational complexity of HJI solutions, we develop a cooperative policy iteration algorithm with guaranteed convergence to Nash equilibria. For scenarios with partially unknown dynamics, a data-driven reinforcement learning approach is proposed, employing a single-critic neural network to learn value functions and policies without prior model knowledge. The framework synergizes game-theoretic control with data-driven learning, enabling scalable synchronization in adversarial settings. Numerical simulations on heterogeneous MASs confirm the approach’s effectiveness in achieving synchronization and optimal disturbance attenuation.