Data-driven Distributed Learning of Multi-agent Systems: A Koopman Operator Approach

Koopman operator theory provides a model-free and purely data-driven technique for studying nonlinear dynamical systems. Since the Koopman operator is infinite-dimensional, researchers have developed several methods that provide a finite-dimensional approximation of the Koopman operator so that it can be applied for practical use cases. One common thing with most of the methods is that their solutions are obtained by solving a centralized minimization problem. In this work, we treat the dynamical system to be a multi-agent system and propose an algorithm to compute the finite-dimensional approximation of the Koopman operator in a distributed manner using the knowledge of the topology of the underlying multi-agent system. The proposed distributed approach results in a sparse Koopman whose block structure mimics the Laplacian of the multi-agent system. Extensive simulation studies illustrate the proposed framework on the network of oscillators and the IEEE 68 bus system.