Source-linked AI summary
Distributed tracking control of leader-follower multi-agent systems under noisy measurement
Jiangping Hu, Gang Feng
TL;DR
Leader-follower tracking is studied when followers have only partial, noisy relative-position measurements and the interconnection topology is directed and time-varying. The paper develops velocity decomposition and distributed estimation, showing mean-square convergence and stochastic stability under stated topology conditions.
Problem
Existing leader-follower control commonly assumes perfect information exchange and undirected follower topology, whereas this paper addresses partial noisy measurements and time-varying directed interconnection.
Method
The paper combines a neighbor-based tracking protocol with distributed active-leader velocity estimation based on a novel velocity decomposition technique.
Results
The proposed scheme achieves mean-square convergence of tracking and velocity-estimation errors, with the closed-loop tracking system stochastically stable in mean square.
Takeaways & Limitations
Distributed tracking can be analyzed for noisy measurements and directed, time-varying topologies under the paper’s stated connectivity and switching conditions.
Takeaways & Limitations
The paper identifies leader-following with more general linear agent dynamics in noisy environments as future research.
Abstract
from arXiv · showhide
In this paper, a distributed tracking control scheme with distributed estimators has been developed for a leader-follower multi-agent system with measurement noises and directed interconnection topology. It is supposed that each follower can only measure relative positions of its neighbors in a noisy environment, including the relative position of the second-order active leader. A neighbor-based tracking protocol together with distributed estimators is designed based on a novel velocity decomposition technique. It is shown that the closed loop tracking control system is stochastically stable in mean square and the estimation errors converge to zero in mean square as well. A simulation example is finally given to illustrate the performance of the proposed control scheme.
1 Introduction
Leader-follower coordination is widely used in multi-agent applications, but existing distributed-control studies commonly assume noise-free measurements. This paper addresses noisy, partial measurements and directed, time-varying topologies with distributed estimation and tracking control.
- Leader-follower coordination has been applied to robotic formation control, UAV formation, and target tracking in sensor networks.
- Existing leader-follower distributed-control studies commonly do not consider measurement noises, despite practical sensor, communication, and quantization disturbances.
- Consensus under noisy measurements had been studied mainly for fixed, undirected network topologies and leaderless first-order systems.
- The paper considers leader-follower tracking under partial and noisy measurements with time-varying directed network topology.
- Its approach combines a novel velocity decomposition technique with a distributed estimator for the active leader’s velocity.
- The estimation errors converge in mean square, and the resulting closed-loop tracking system is stochastically stable in mean square.
- The paper analyzes tracking control and stochastic stability before presenting a numerical example.
2 Problem formulation
The paper formulates leader-follower tracking over directed graphs whose topology may switch, while followers use noisy relative measurements and estimate the leader’s unmeasured velocity. The objective is mean-square tracking with vanishing velocity-estimation errors.
- 2.1 Preliminaries: A directed graph represents information flow among one leader, labeled 0, and n follower agents.
- 2.1 Preliminaries: The leader adjacency matrix B records which followers receive communication links from the leader, and H is defined as L+B.
- 2.1 Preliminaries: A globally reachable leader allows leader information to propagate through the network, a weaker condition than strong connectivity.
- 2.1 Preliminaries: The topology switches among finitely many directed graphs through a piecewise-constant signal, with each topology held for at least a positive dwell time τ.
- 2.2 Leader-following problem: Followers have first-order dynamics, while the active leader has second-order dynamics with position x0, velocity v0, acceleration a0, and output y0=x0.
- 2.2 Leader-following problem: Practical information exchange is constrained by sensor and communication limitations, so follower measurements are noisy rather than perfect.
- 2.2 Leader-following problem: Because followers cannot measure v0 directly, each estimates it from noisy neighbor measurements for control design.
- 2.2 Leader-following problem: The formulation seeks asymptotic mean-square leader tracking, mean-square convergence of velocity-estimation errors, and mean-square stochastic stability of the closed loop.
3 Distributed control of leader-follower system
The paper develops a distributed tracking controller and leader-velocity estimator for noisy relative measurements, using velocity decomposition under directed network topologies. Mean-square tracking and estimation convergence are established for fixed and suitably switching topologies.
- Problem: The controller addresses relative-position measurements corrupted by sensor noise, quantization errors, and related communication constraints.Each follower uses noisy information from neighboring agents, including measurements involving the active leader.
- Velocity decomposition: A novel velocity decomposition introduces a nominal leader velocity and gain function α(t) to support distributed estimation from partial noisy measurements.The function α(t) is assumed continuously differentiable, bounded, and subject to the stated integral conditions.
- Distributed control: The local dynamic control scheme combines neighbor-based tracking with a distributed estimator of the active leader’s nominal velocity.The estimator aggregates neighboring relative-position information over time and predicts the leader’s trajectory through an integrator.
- Time-invariant topology: For a time-invariant topology, if vertex 0 is globally reachable, every follower tracks the active leader asymptotically in mean square.The analysis uses an Itô stochastic differential equation and a Lyapunov function to establish the result.
- Convergence analysis: The gain function α(t) ensures the required decay term and yields convergence of the Lyapunov expectation, improving the stated tracking result over prior directed-topology work.The paper also reports convergence of the velocity estimation error in mean square.
- Time-varying topology: For time-varying topology, mean-square tracking holds when the leader is globally reachable and the follower subgraph is balanced on each switching interval.Balance is sufficient, while the numerical example indicates it is not necessary for mean-square convergence of tracking errors.
4 A simulation example
The simulation tests the proposed tracking control on a three-follower system with switching directed topologies and noisy measurements. Tracking errors converge in mean square, including when one follower subgraph is unbalanced.
- Simulation setup: The example uses one active leader and three followers with a switching topology sequence G1, G2, G1, G2, · · ·.The two topologies are described in Fig. 1.
- Simulation setup: The leader adjacency matrices are B1 = diag{1, 0, 0} and B2 = diag{1, 0, 1}, with minimal eigenvalue ¯λ = 0.3187 for H1 and H2.
- Tracking performance: The tracking errors ¯x1(t), ¯x2(t), and ¯x3(t) are shown in Fig. 2 under noisy measurements.The initial value of ε(t) is randomly selected as col(2, 1, −1, −0.2, −2, 0.2).
- Tracking performance: The tracking control ensures that the followers track the active leader under noisy measurements.
- Tracking performance: The tracking errors still converge in mean square even though digraph Gf1 is not balanced.
5 Conclusions
The paper studies leader-following control with measurement noises and directed interconnection topology using distributed control and estimators. It concludes with mean-square convergence analysis and identifies more general linear-agent dynamics as future work.
- The paper develops a neighbor-based distributed control scheme with distributed estimators for leader-following systems with measurement noises and directed interconnection topology.
- Algebraic graph theory and stochastic analysis are used to analyze mean-square convergence of the tracking errors.
- A future research direction is leader-following control in noisy environments when each agent has more general linear dynamics.