Distributed Optimization for Heterogeneous Integrator Chain Multi-agent Systems with Mismatched Disturbances

This paper presents a novel approach to address distributed optimization in high-order heterogeneous multi-agent systems, particularly focusing on scenarios involving mismatched disturbances. The proposed method eliminates the need for global knowledge of local objective functions by utilizing real-time gradient measurements from system outputs. It integrates an optimal signal generator and a tracking controller seamlessly, creating a cohesive structural design. A distinctive feature is the incorporation of a disturbance observer within the controller, effectively mitigating the impact of mismatched disturbances. The effectiveness of the theoretical findings are demonstrated through a comprehensive analysis of the composite Lyapunov function associated with the closed-loop system. Additionally, numerical examples validate the robustness of this innovative approach.