[Paper Review] Distributed H-infinity Tracking Control for Discrete-Time Multi-Agent Systems with a High-Dimensional Leader

Guanghui Wen, Valery Ugrinovskii|arXiv (Cornell University)|Aug 30, 2013

Distributed Control Multi-Agent Systems13 references3 citations

TL;DR

This paper proposes a distributed H∞ tracking control protocol for discrete-time multi-agent systems with a high-dimensional leader, using neighbor-based state estimation and dynamic control laws to achieve robust leader-following tracking under partial leader state measurement and external disturbances. The key contribution is a design procedure based on a modified algebraic Riccati equation that ensures H∞ performance under detectability and directed spanning tree conditions.

ABSTRACT

This paper considers the distributed H-infinity leader-following tracking problem for a class of discrete time multi-agent systems with a high-dimensional dynamic leader. It is assumed that output information about the leader is only available to designated followers, and the dynamics of the followers are subject to perturbations. To achieve distributed H-infinity leader-following tracking, a new class of control protocols is proposed which is based on the feedback from the nearest neighbors as well as a distributed state estimator. Under the assumptions that dynamics of the leader are detectable and the communication topology contains a directed spanning tree, sufficient conditions are obtained that enable all followers to track the leader while achieving a desired H-infinity leader-following tracking performance. Numerical simulations illustrate the effectiveness of the theoretical analysis.

Motivation & Objective

• To address the leader-following tracking problem in discrete-time multi-agent systems where the leader has higher-dimensional dynamics than the followers.
• To design a distributed control protocol that enables followers to track the leader using only local neighbor information and partial leader measurements.
• To achieve a specified H∞ performance level despite external disturbances and unmeasurable leader states.
• To extend existing consensus tracking frameworks to non-identical agent dynamics and partial leader observation.
• To develop a dynamic protocol integrating local controllers and distributed state estimators for robust performance.

Proposed method

• A dynamic control protocol is designed using a local controller and a neighbor-based distributed state estimator for each follower.
• The protocol is based on solving a modified algebraic Riccati equation derived from H∞ control theory.
• The state estimator enables each follower to estimate the unmeasurable states of the high-dimensional leader using information from neighbors.
• The design ensures H∞ performance by satisfying a linear matrix inequality (LMI) condition with a given disturbance attenuation level γ.
• The communication topology is modeled as a directed graph with a spanning tree rooted at the leader, ensuring information flow to all followers.
• The performance variable e(k) is defined via a matrix C, which can be set to identity for tracking error minimization.

Experimental results

Research questions

• RQ1 How can distributed H∞ tracking be achieved in multi-agent systems where the leader has higher-dimensional dynamics than the followers?
• RQ2 What control protocol structure enables robust tracking performance under partial leader state measurement and external disturbances?
• RQ3 Under what graph topology and system conditions can H∞ leader-following tracking be guaranteed?
• RQ4 How can a distributed state estimator be designed to enable followers to estimate the leader’s unmeasurable states?
• RQ5 What role does the modified algebraic Riccati equation play in achieving the desired H∞ performance?

Key findings

• The proposed protocol ensures asymptotic leader-following tracking in the absence of disturbances, as confirmed by simulation trajectories in Figs. 2–4.
• The H∞ performance level γ = 1 is achieved, as demonstrated by the energy ratio in Fig. 6, where the disturbance attenuation is maintained below the threshold.
• The eigenvalues of the matrix 𝔻̂ are bounded with λ₀ = 0.8579 < 1, indicating stability of the error dynamics.
• The LMI solution yields V = (-0.8698, 0.2105, 0.1083) and F = (0.0003, 0.0551, 0.4660)ᵀ with ε = 0.25, enabling the control design.
• The system achieves H∞ performance when the leader is detectable and the communication graph contains a directed spanning tree rooted at the leader.
• Numerical simulations confirm that the protocol ensures both consensus tracking and disturbance attenuation under zero initial conditions.