Distributed Koopman Learning using Partial Trajectories for Control

TL;DR

The paper tackles learning unknown nonlinear dynamics in a multi-agent system from partially observed data while preserving data privacy. It introduces Distributed Deep Koopman Learning using Partial Trajectories (DDKL-PT), a two-step, consensus-based optimization that yields a global Koopman representation across agents without sharing raw trajectories, followed by an MPC framework that uses the learned dynamics for surface-vehicle control. The key contributions are (i) a distributed algorithm that achieves consensus on matrices $A,B,C$ and lift parameters $oldsymbol{ heta}$ from partial data, and (ii) integration of the learned Koopman model with kinematics to enable model-based control, demonstrated on a surface-vehicle scenario with successful tracking and station-keeping. The results indicate that DDKL-PT can scale to large MAS settings, preserve data locality, and provide sufficiently accurate dynamics for effective MPC in practical autonomous systems.

Abstract

This paper proposes a distributed data-driven framework for dynamics learning, termed distributed deep Koopman learning using partial trajectories (DDKL-PT). In this framework, each agent in a multi-agent system is assigned a partial trajectory offline and locally approximates the unknown dynamics using a deep neural network within the Koopman operator framework. By exchanging local estimated dynamics rather than training data, agents achieve consensus on a global dynamics model without sharing their private training trajectories. Simulation studies on a surface vehicle demonstrate that DDKL-PT attains consensus with respect to the learned dynamics, with each agent achieving reasonably small approximation errors over the testing data. Furthermore, a model predictive control scheme is developed by integrating the learned Koopman dynamics with known kinematic relations. Results on goal-tracking and station-keeping tasks support that the distributedly learned dynamics are sufficiently accurate for model-based optimal control.

Figures (4)

• Figure 1: Illustration of the distributed Koopman learning, where each agent is only available for a partial trajectory.
• Figure 2: Five-agent connected network with self-arcs, where self-arcs are omitted for simplicity.
• Figure 3: Consensus of the DDKR of each agent $i$ during the learning process, where the solid black line denotes the average of the $10$ experiments, and the blue shadow denotes the standard deviation.
• Figure 4: Tracking errors of each agent in MAS driven by DDKL-PT-MPC