Distributed Consensus of Linear Multi-Agent Systems with Adaptive Dynamic Protocols

This paper considers the distributed consensus problem of multi-agent systems with general continuous-time linear dynamics. Two distributed adaptive dynamic consensus protocols are proposed, based on the relative output information of neighboring agents. One protocol assigns an adaptive coupling weight to each edge in the communication graph while the other uses an adaptive coupling weight for each node. These two adaptive protocols are designed to ensure that consensus is reached in a fully distributed fashion for any undirected connected communication graphs without using any global information. A sufficient condition for the existence of these adaptive protocols is that each agent is stabilizable and detectable. The cases with leader-follower and switching communication graphs are also studied.

💡 Research Summary

The paper addresses the distributed consensus problem for multi‑agent systems whose agents follow general continuous‑time linear dynamics. Existing consensus protocols for such systems often require global knowledge of the communication graph, specifically the second smallest eigenvalue (λ₂) of the Laplacian matrix, which is impractical for fully distributed implementation. To overcome this limitation, the authors propose two novel adaptive dynamic consensus protocols that rely only on relative output information from neighboring agents.

The first protocol assigns an adaptive coupling weight c₍ᵢⱼ₎(t) to each edge of the undirected communication graph. Each agent i maintains an internal protocol state vᵢ∈ℝⁿ and computes its control input as uᵢ=Fvᵢ. The dynamics of vᵢ are driven by the nominal closed‑loop matrix (A+BF) and a correction term proportional to the output error yᵢ−yⱼ−C(vᵢ−vⱼ). The edge weight c₍ᵢⱼ₎ is updated by a gradient‑like law involving the squared norm of this error weighted by a symmetric positive‑semi‑definite matrix Γ, with a positive adaptation gain κ₍ᵢⱼ₎. This mechanism guarantees that the edge weights monotonically increase and converge to finite limits while the protocol states converge to zero, leading to consensus.

The second protocol uses a node‑based adaptive weight dᵢ(t). Here each agent i keeps a protocol state \tilde vᵢ and computes uᵢ=F\tilde vᵢ. The update of \tilde vᵢ contains a term dᵢ∑ⱼ aᵢⱼ