Self-Supervised Koopman Operator-Learning of Nonlinear Multi-Agent Systems With Partial Information

A hybrid self-supervised Koopman deep learning algorithm has been developed to learn the Koopman operator for nonlinear multi-agent systems (MASs) using partial state information. In contrast, most existing Koopman operator-learning methods rely on full state series, which is infeasible for most general nonlinear networked systems or multi-agent systems (MASs), as each node/agent only has access to its neighbor(s). Therein, a nonlinear encoder is designed as an observer function to lift the nonlinear state into a high-dimensional Hilbert space. In this lifted linear space, a linear networked model is constructed to predict future states. A corresponding nonlinear decoder, serving as the inverse of the encoder, retrieves the original nonlinear states. This algorithm could distill the linear features from the partial state information of nonlinear MASs, transforming complex, hard-to-predict nonlinear dynamics into high-dimensional linear systems. Accordingly, the retrieved linear feature can serve as an interface for other calculations, which can then be decoded back to the original nonlinear states. Theoretical derivation guarantees the feasibility of the present distributed Koopman operator-learning (DKOL). Extensive numerical simulations demonstrate its effectiveness and superiority. © 2025 IEEE.