Exact Leader Estimation: A New Approach for Distributed Differentiation

2025-02-13

AI Summary

This paper addresses the distributed high-order derivative estimation problem for multi-agent systems without explicit leader identification. To handle realistic constraints—including unknown leaders, sampled-data communication, and bounded measurement noise—we propose a distributed observer protocol based on Levant’s homogeneous differentiators. Each agent exchanges only scalar information and executes a uniform algorithm (except the leader), enabling finite-time exact estimation of any $m$-th order derivative of the leader’s signal. To the best of our knowledge, this is the first work to jointly model sampled-data communication and bounded noise within a distributed leader–follower framework, and to derive a tight worst-case steady-state accuracy bound. We rigorously prove the protocol’s robustness, finite-time exactness, and fully distributed nature—requiring no global network information. Numerical experiments on second- and fourth-order systems demonstrate finite-time convergence for first- and third-order derivative estimation, along with strong noise resilience.

Technology Category

Intelligent Robots: State EstimationMultiagent Systems: Distributed Problem SolvingSearch and Optimization: Distributed Search

Application Category

Security and Privacy: Large-scale security measurementsSystems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deploymentsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

A novel strategy aimed at cooperatively differentiating a signal among multiple interacting agents is introduced, where none of the agents needs to know which agent is the leader, i.e. the one producing the signal to be differentiated. Every agent communicates only a scalar variable to its neighbors; except for the leader, all agents execute the same algorithm. The proposed strategy can effectively obtain derivatives up to arbitrary $m$-th order in a finite time under the assumption that the $(m+1)$-th derivative is bounded. The strategy borrows some of its structure from the celebrated homogeneous robust exact differentiator by A. Levant, inheriting its exact differentiation capability and robustness to measurement noise. Hence, the proposed strategy can be said to perform robust exact distributed differentiation. In addition, and for the first time in the distributed leader-observer literature, sampled-data communication and bounded measurement noise are considered, and corresponding steady-state worst-case accuracy bounds are derived. The effectiveness of the proposed strategy is verified numerically for second- and fourth-order systems, i.e., for estimating derivatives of up to first and third order, respectively.

Problem

• Distributed signal differentiation among agents
• Leader estimation without leader identification
• Robust exact differentiation under noise

Innovation

• Distributed signal differentiation strategy
• Scalar variable communication
• Robust exact differentiation capability