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A Framework on Fully Distributed State Estimation and Cooperative Stabilization of LTI Plants

Peihu Duan, Yuezu Lv, Guanghui Wen, Maciej Ogorzałek

TL;DR

This work tackles fully distributed state estimation and cooperative stabilization for a multi-agent LTI plant connected by a directed graph. It introduces a novel fully distributed estimator–controller framework in which each node runs an output estimator with an adaptive coupling gain and a local observer, coordinated through local interactions so that the estimates converge to the global state and the plant stabilizes, while the global topology information is not required. Key contributions include: (i) fully distributed state estimation and stabilization over directed graphs, (ii) adaptive coupling gains to replace dependence on global topology, (iii) distributed LMIs for gains design, (iv) extension to pure state estimation, and (v) a sigma-modification robust design and accompanying proofs, validated by simulations on planar transportation and large sensor networks. This framework enhances scalability and resiliency in swarm-like multi-agent systems by avoiding central coordination and reducing communication frequency while maintaining stability and performance under disturbances.

Abstract

How to realize high-level autonomy of individuals is one of key technical issues to promote swarm intelligence of multi-agent (node) systems with collective tasks, while the fully distributed design is a potential way to achieve this goal. This paper works on the fully distributed state estimation and cooperative stabilization problem of linear time-invariant (LTI) plants with multiple nodes communicating over general directed graphs, and is aimed to provide a fully distributed framework for each node to perform cooperative stabilization tasks. First, by incorporating a novel adaptive law, a consensus-based estimator is designed for each node to obtain the plant state based on its local measurement and local interaction with neighbors, without using any global information of the communication topology. Subsequently, a local controller is developed for each node to stabilize the plant collaboratively with performance guaranteed under mild conditions. Specifically, the proposed method only requires that the communication graph be strongly connected, and the plant be collectively controllable and observable. Further, the proposed method can be applied to pure fully distributed state estimation scenarios and modified for noise-bounded LTI plants. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.

A Framework on Fully Distributed State Estimation and Cooperative Stabilization of LTI Plants

TL;DR

This work tackles fully distributed state estimation and cooperative stabilization for a multi-agent LTI plant connected by a directed graph. It introduces a novel fully distributed estimator–controller framework in which each node runs an output estimator with an adaptive coupling gain and a local observer, coordinated through local interactions so that the estimates converge to the global state and the plant stabilizes, while the global topology information is not required. Key contributions include: (i) fully distributed state estimation and stabilization over directed graphs, (ii) adaptive coupling gains to replace dependence on global topology, (iii) distributed LMIs for gains design, (iv) extension to pure state estimation, and (v) a sigma-modification robust design and accompanying proofs, validated by simulations on planar transportation and large sensor networks. This framework enhances scalability and resiliency in swarm-like multi-agent systems by avoiding central coordination and reducing communication frequency while maintaining stability and performance under disturbances.

Abstract

How to realize high-level autonomy of individuals is one of key technical issues to promote swarm intelligence of multi-agent (node) systems with collective tasks, while the fully distributed design is a potential way to achieve this goal. This paper works on the fully distributed state estimation and cooperative stabilization problem of linear time-invariant (LTI) plants with multiple nodes communicating over general directed graphs, and is aimed to provide a fully distributed framework for each node to perform cooperative stabilization tasks. First, by incorporating a novel adaptive law, a consensus-based estimator is designed for each node to obtain the plant state based on its local measurement and local interaction with neighbors, without using any global information of the communication topology. Subsequently, a local controller is developed for each node to stabilize the plant collaboratively with performance guaranteed under mild conditions. Specifically, the proposed method only requires that the communication graph be strongly connected, and the plant be collectively controllable and observable. Further, the proposed method can be applied to pure fully distributed state estimation scenarios and modified for noise-bounded LTI plants. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.
Paper Structure (21 sections, 9 theorems, 106 equations, 8 figures, 1 algorithm)

This paper contains 21 sections, 9 theorems, 106 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review and Motivations
  3. Contributions
  4. Organization and Notations
  5. Problem Formulation
  6. Model Description
  7. Graph Theory
  8. Estimator and Controller Structure
  9. Fully distributed state estimation and cooperative stabilization design
  10. State Estimation and Stabilization Control Performance Analysis
  11. Estimator and Controller Gains Design
  12. Application to Pure State Estimation
  13. Robust Estimator and Controller Design
  14. Simulation
  15. Conclusion
  16. ...and 6 more sections

Key Result

Lemma 1

Suppose that Assumption assp2 holds. Then, the matrix is a non-singular $M$-matrix, where $\mathcal{L}$ is the Laplacian matrix of $\mathcal{G}$ and $\mathcal{A}^j=\text{diag}(a_{1j}$, $\ldots$, $a_{Nj})$. Moreover, the matrix is a non-singular $M$-matrix, where $m=\sum_{i=1}^Nm_i$ and $\hat{\mathcal{A}}=\text{diag}(\mathcal{A}_1$, $\ldots$, $\mathcal{A}_N)$ with $\mathcal{A}_i=\text{diag}(a_{i1

Figures (8)

  • Figure 1: Six mobile robots carry a huge plant cooperatively.
  • Figure 2: The position and velocity errors of the plant under the proposed FDCS (\ref{['hatyij']})-(\ref{['ui']}), where $x(t) = [p_1(t) - p_{\text{des},1}$, $p_2(t) - p_{\text{des},2}$, $v_1(t)$, $v_2(t) ]^T$.
  • Figure 3: The trajectories of the noisy plant under different cooperative control methods, where the filled square and circle represent the initial and terminal positions, respectively.
  • Figure 4: The coupling gains of different cooperative control methods, where $\bar{\gamma} = \frac{1}{6}\sum_{i=1}^{6} \gamma_i$ denotes the average coupling gain in the FDCS.
  • Figure 5: The communication topology of 100 sensors, where two nodes are neighbors if the distance between them is less than 60 in the coordinate-frame scale.
  • ...and 3 more figures

Theorems & Definitions (15)

  • Remark 1
  • Definition 1
  • Lemma 1
  • Lemma 2
  • Remark 2
  • Remark 3
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • ...and 5 more