Generalized Distributed Optimal Coordination for Multiagent Systems via Weak Coupling Hierarchical Control Framework

In this article, we reformulate the distributed optimal coordination problem for multi-agent systems to broaden its applicability across a wider range of coordination scenarios, thereby introducing a Generalized Distributed Optimal Coordination (GDOC) problem. In GDOC, the inter-agent relationships evolve from equality (consensus) to affinity (coordination), while local cost functions are unified as blends of parameters and shared basis functions, enabling cohesive network optimization. To address the GDOC problem, we propose a weak coupling hierarchical control framework for heterogeneous multi-agent systems. This framework consists of three layers: a signal generator, a tracking controller, and a speed regulator. For the generator, a transformed consensus protocol is designed for agents to estimate the global cost function and feasible set in a distributed manner, with the gradient projection method applied to minimize the objective function locally. For the controller, an observer-based output feedback control law is designed through system decomposition. For the regulator, a dynamic adaptive parameter is introduced to adjust the updating speed of the reference signal based on the agent’s relative tracking ability. The proposed framework not only preserves the universality of hierarchical control but also addresses the limitation of topdown structural open-loop control by introducing a regulator to form a bottom-up feedback loop. Finally, the effectiveness of the proposed framework is verified by Lyapunov stability theory analysis and simulation experiments. Note to Practitioners—In numerous task scenarios, the coordinated control of multi-agent systems involves solving optimization problems. This paper proposes GDOC to mathematically characterize these scenarios in a unified way, with the goal of controlling each agent’s output to converge towards the minimum point of the aggregate cost functions while maintaining preset inter-agent relationships. To achieve this, the affine transformation matrix is introduced to describe these inter-agent relationships under diverse coordination scenarios. Furthermore, the cost function adopts a form involving parameters and shared basis functions, facilitating interaction and iteration within the cost function. Correspondingly, an engineering-friendly control framework is proposed to address the GDOC problem. This framework consists of a reference signal generator, a tracking controller, and a speed regulator, each of which can be designed separately. The speed regulator is a new addition, aimed at adjusting the updating speed of signals according to the physical dynamic response capability of each agent, thereby establishing an indirect bottom-up feedback loop. This control framework can be applied to addressing GDOC problems in situations with switching cost functions and multiple solutions.