This paper aims to solve the optimal consensus problem for homogeneous systems of general linear dynamics and a cost function. Specifically, we present a new method rooted in LQ optimal control theory and observer design. This method is fundamentally different from the existing consensus control algorithms, which rely on nonzero eigenvalues of the communication topology to determine the distributed controller. The analytical solution for the distributed controller is derived via Riccati equations and observers, which is parallel to the classical optimal control theory. Theoretical analysis and a simulation example demonstrate that the proposed optimal consensus method achieves significantly faster convergence than conventional approaches. Notably, this framework can be extended to tackle consensus problems in heterogeneous multi-agent systems. 1 | Introduction The distributed cooperative control problem for multi-agent systems has recently garnered significant attention from various scientific communities. Through communication topologies, multiple agents can coordinate to solve tasks that are infeasible for a single agent, with applications spanning distributed robotics, unmanned aerial vehicles, wireless sensor networks, and satellite formation [1–4]. In this context, achieving consensus is a fundamental problem, requiring the design of distributed control protocols that guide all agents to agree on specific variables [5, 6]. As a result, numerous researchers have
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