Optimal cooperative output regulation with norm-based performance specifications

This article addresses the optimal cooperative output regulation problem for linear heterogeneous multi-agent systems, ensuring both transient and steady-state performance of regulated errors while minimizing the predefined cost. To achieve the explicit specifications on the regulated error even if not all agents can directly access the regulated error, we construct a hierarchical "observation-control" framework. At the observation layer, by imposing constraints on the norms of relative observation states, a distributed edge-based observer is developed to reproduce the states of the exosystem with explicitly prescribed transient performance. At the control layer, by employing a data-driven actor-critic learning algorithm and the prescribed performance control, we derive an optimal control scheme that enforces prescribed constraints on auxiliary tracking error norms and minimizes the predefined cost without solving the nonlinear Hamilton-Jacobi-Bellman equation. Through indirect specifications on observation and auxiliary tracking errors, the multi-dimensional regulated errors converge to a predefined residual set within a specified time, reducing the computational burden of decoupling. Finally, experimental results validate the effectiveness of the proposed control scheme.