[Paper Review] Novel Distributed Robust Adaptive Consensus Protocols for Linear Multi-agent Systems with Directed Graphs and External Disturbances

Yuezu Lv, Zhongkui Li+2 more|arXiv (Cornell University)|Nov 4, 2015

Distributed Control Multi-Agent Systems20 references4 citations

TL;DR

This paper proposes novel distributed robust adaptive consensus protocols for linear multi-agent systems with directed communication graphs and external disturbances. By introducing additive functions into the adaptive law, the method ensures ultimate boundedness of both consensus error and adaptive weights, achieving fully distributed, robust leader-follower consensus without requiring global graph knowledge or matching condition constraints on disturbances.

ABSTRACT

This paper addresses the distributed consensus protocol design problem for linear multi-agent systems with directed graphs and external unmatched disturbances. A novel distributed adaptive consensus protocol is proposed to achieve leader-follower consensus for any directed graph containing a directed spanning tree with the leader as the root node. It is noted that the adaptive protocol might suffer from a problem of undesirable parameter drift phenomenon when bounded external disturbances exist. To deal with this issue, a distributed robust adaptive consensus protocol is designed to guarantee the ultimate boundedness of both the consensus error and the adaptive coupling weights in the presence of external disturbances. Both adaptive protocols are fully distributed, relying on only the agent dynamics and the relative states of neighboring agents.

Motivation & Objective

• To design a fully distributed adaptive consensus protocol for linear multi-agent systems with directed graphs containing a directed spanning tree.
• To address the parameter drift phenomenon in adaptive protocols under bounded external disturbances.
• To develop a robust adaptive protocol that guarantees ultimate boundedness of consensus error and adaptive coupling weights under general unmatched disturbances.
• To eliminate the need for global information such as eigenvalue knowledge of the Laplacian matrix.
• To extend existing adaptive protocols to general directed graphs and non-matching disturbances, overcoming limitations in prior works.

Proposed method

• Proposes a novel distributed adaptive protocol using additive functions instead of multiplicative ones, enabling simpler quadratic Lyapunov function analysis.
• Introduces a robust adaptive protocol with modified update laws that incorporate disturbance bounds and adaptive gains to counteract parameter drift.
• Employs a Lyapunov-based stability analysis to prove ultimate boundedness of consensus error and adaptive weights under external disturbances.
• Uses linear matrix inequalities (LMIs) to design feedback gain matrices K and Γ for the control protocol.
• Relies solely on local agent dynamics and relative state information between neighbors, ensuring full distributability.
• Applies a modified adaptive law with time-varying coupling weights $ d_i $, updated based on local consensus error and disturbance estimates.

Experimental results

Research questions

• RQ1 Can a fully distributed adaptive consensus protocol be designed for general linear multi-agent systems with directed communication graphs?
• RQ2 How can the parameter drift phenomenon in adaptive protocols be mitigated under bounded external disturbances?
• RQ3 Can robustness be achieved for general unmatched disturbances without requiring the matching condition?
• RQ4 Is it possible to replace complex integral-like Lyapunov functions with simpler quadratic forms in stability analysis?
• RQ5 What are the existence conditions for the proposed adaptive protocols under directed graphs and disturbances?

Key findings

• The proposed adaptive protocol achieves leader-follower consensus for any directed graph containing a directed spanning tree with the leader as root, using only local information.
• The robust adaptive protocol ensures ultimate boundedness of both consensus error $ \xi $ and adaptive coupling weights $ d_i $, even under general bounded external disturbances.
• The upper bound of the consensus error depends on agent dynamics, communication graph structure, disturbance bounds, and design parameters $ \varphi_i $, which can be tuned to achieve acceptable performance.
• The method avoids the need for global information such as the smallest nonzero eigenvalue of the Laplacian matrix, making it fully distributed.
• Compared to prior works, the proposed protocol is applicable to non-matching disturbances and uses a simpler quadratic Lyapunov function, unlike the integral-like functions in earlier studies.
• Simulation results confirm bounded consensus errors and adaptive weights under disturbances, validating the theoretical claims.