Abstract: A distributed online algorithm based on proximal gradient descent is proposed to study the distributed online composite optimization problem with time-varying regularization terms for heterogeneous linear multi-agent systems. This algorithm ensures that the input and state of the agent remain within the constraint set at any given time. In order to evaluate the performance of the proposed algorithm, the dynamic regret performance is analyzed, and the upper bound related to time and path length is obtained. If the path length increases sublinearly with time, the upper bound of dynamic regret also increases sublinearly with time, which theoretically proves the effectiveness of the algorithm. The performance and theoretical results of the algorithm are verified through simulations.