Source-linked AI summary
Distributed Observers Design for Leader-Following Control of Multi-Agent Networks (Extended Version)
Yiguang Hong, Guanrong Chen, Linda Bushnell
TL;DR
The paper addresses leader-following when an active leader’s velocity cannot be measured and the interconnection topology switches. It designs reduced-order distributed observers and neighbor-based controllers, proving leader tracking and estimating errors under disturbances.
Problem
The paper studies leader-following for second-order followers when the active leader’s velocity is difficult to measure in real time and the network topology switches.
Method
It combines first-order distributed observers with dynamic neighbor-based controllers and constructs a common Lyapunov function for the switching network.
Results
The distributed control guarantees leader-following in a switching network topology, while tracking error is evaluated in a noisy environment.
Takeaways & Limitations
Agents can follow the active leader using distributed observer and control rules even when the leader velocity is not directly available.
Takeaways & Limitations
The analysis assumes a minimum dwell time between topology switches and that the leader input may be known to all agents while its velocity is not measured.
Abstract
from arXiv · showhide
This paper is concerned with a leader-follower problem for a multi-agent system with a switching interconnection topology. Distributed observers are designed for the second-order follower-agents, under the common assumption that the velocity of the active leader cannot be measured in real time. Some dynamic neighbor-based rules, consisting of distributed controllers and observers for the autonomous agents, are developed to keep updating the information of the leader. With the help of an explicitly constructed common Lyapunov function (CLF), it is proved that each agent can follow the active leader. Moreover, the tracking error is estimated even in a noisy environment. Finally, a numerical example is given for illustration.
1 Introduction
Distributed observer design is motivated by the limited theoretical results for measurement-based neighbor control and the need to track an active leader with unknown velocity in second-order agents under switching topologies.
- Distributed estimation through observers is important for multi-agent coordination, with applications especially in sensor and robot networks.
- Few theoretical results address distributed observers and measurement-based dynamic neighbor-based control design.
- The work extends conventional observer design to distributed observers for an active leader moving with unknown velocity.
- The considered agents are second-order, and switching inter-agent topologies are handled through construction of a common Lyapunov function.The approach reduces observer order to simplify construction of the common Lyapunov function.
2 Preliminaries
The preliminaries specify a leader-follower network, switching-topology assumptions, active-leader dynamics with position as the only measurable state, and disturbed second-order follower agents.
- The network contains one leader and n follower-agents, with connectivity requiring a leader-directed connection into every follower component.
- Topology switching occurs over bounded non-overlapping intervals with a minimum dwell time τ between successive switches.
- Neighbor sets, interconnection weights, the follower Laplacian, and leader connection weights define the time-varying network structure.
- The leader is active, its state changes throughout the process, and only its position-related output y is measurable while velocity v0 is difficult to measure in real time.The leader input u0(t) may be regarded as a policy known to all agents.
- Follower agents are modeled as second-order systems with bounded disturbances, and the objective is for all followers to keep the leader’s pace.
3 Main Results
The paper develops distributed observer-controller rules for second-order followers under switching topologies and analyzes leader tracking using a common Lyapunov function. It proves asymptotic tracking without disturbances and bounded tracking error under disturbances, with a numerical illustration.
- Distributed observer-controller design: The proposed distributed controller and first-order observer use only local information from each agent and its neighbors.The observer estimates the leader’s unmeasurable velocity while the controller uses the estimate for tracking.
- Distributed observer-controller design: The observer design can be generalized with an adjustable parameter, providing additional freedom for distributed-observer tuning.The generalized design replaces l/k^2 with an adjustable parameter k0.
- Noise-free tracking: Under noise-free conditions and connected switching graphs, suitable constants k and l make followers track the leader in both position and speed.The result is established using the closed-loop error system and a common Lyapunov function.
- Noise-free tracking: The explicitly constructed common Lyapunov function yields exponential decay of the error measure on each connected interval.The analysis obtains V(z(t)) ≤ V(z(t_i))e^-2β(t−t_i) and a global bound of the form V(z(t)) ≤ V(z(0))e^-2βt.
- Disturbed tracking: With disturbances, if the total connected period is sufficiently large, each agent’s tracking error remains bounded and the bound tends to zero as the disturbance magnitude tends to zero.Theorem 2 introduces cδ > 0 with lim∆→0 cδ = 0.
- Numerical illustration: A four-follower simulation with switching period 0.2, k = 200, l = 40, and u0 = cos(t) shows noise-free tracking and bounded errors with disturbances.The figure compares position tracking errors in the noise-free and disturbed cases.
4 Conclusions
The paper proposes neighbor-based observers and dynamic coordination for mobile agents following an active leader with unknown velocity in switching networks. It proves leader-following and evaluates tracking error in noisy environments.
- A neighbor-based observer design and dynamic coordination rule are proposed for autonomous agents.
- The distributed control guarantees leader-following in a switching network topology.
- The paper evaluates the tracking error even in a noisy environment.