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Distributed State Estimation for Discrete-time LTI Systems: the Design Trilemma and a Novel Framework

Ruixuan Zhao, Guitao Yang, James Fleming, Boli Chen

Abstract

With the advancement of IoT technologies and the rapid expansion of cyber-physical systems, there is increasing interest in distributed state estimation, where multiple sensors collaboratively monitor large-scale dynamic systems. Compared with its continuous-time counterpart, a discrete-time distributed observer faces greater challenges, as it cannot exploit high-gain mechanisms or instantaneous communication. Existing approaches depend on three tightly coupled factors: (i) system observability, (ii) communication frequency and dimension of the exchanged information, and (iii) network connectivity. However, the interdependence among these factors remains underexplored. This paper identifies a fundamental trilemma among these factors and introduces a general design framework that balances them through an iterative semidefinite programming approach. As such, the proposed method mitigates the restrictive assumptions present in existing works. The effectiveness and generality of the proposed approach are demonstrated through a simulation example.

Distributed State Estimation for Discrete-time LTI Systems: the Design Trilemma and a Novel Framework

Abstract

With the advancement of IoT technologies and the rapid expansion of cyber-physical systems, there is increasing interest in distributed state estimation, where multiple sensors collaboratively monitor large-scale dynamic systems. Compared with its continuous-time counterpart, a discrete-time distributed observer faces greater challenges, as it cannot exploit high-gain mechanisms or instantaneous communication. Existing approaches depend on three tightly coupled factors: (i) system observability, (ii) communication frequency and dimension of the exchanged information, and (iii) network connectivity. However, the interdependence among these factors remains underexplored. This paper identifies a fundamental trilemma among these factors and introduces a general design framework that balances them through an iterative semidefinite programming approach. As such, the proposed method mitigates the restrictive assumptions present in existing works. The effectiveness and generality of the proposed approach are demonstrated through a simulation example.
Paper Structure (6 sections, 2 theorems, 25 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 6 sections, 2 theorems, 25 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Literature Review
  4. Proposed Distributed Observer Design
  5. Simulation Examples
  6. Conclusions and Future Works

Key Result

Theorem 1

Consider an LTI system eq:sys, the communication among all sensor nodes is described by the graph $\mathcal{G}$ and follows Assumption assum:trans. For each node, the local observer eq:observer can reconstruct the entire system state $x(t)$ asymptotically as eq:full-converge if there exists a positi holds, where $\mathbf{W}=[\varpi_{ij}]_{i,j\in\mathbf{N}}\in\mathbb{R}^{N\times N}$ ($\varpi_{ij}=0

Figures (5)

  • Figure 1: Distributed observer framework with five nodes. Each observer $\mathcal{O}_i$ uses its local measurement $y_i$ and information from neighbors via the cyan dashed communication links.
  • Figure 2: Trilemma for discrete-time distributed state estimation on LTI plant with static graph.
  • Figure 3: (Left) Two timescale structure; (Right) Single timescale structure.
  • Figure 4: Communication topologies for simulation examples
  • Figure 5: Norm of estimation errors at each node for (a) enhanced observability, and (b) enhanced network connectivity.

Theorems & Definitions (5)

  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Remark 1