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Stability Conditions for Remote State Estimation of Multiple Systems over Multiple Markov Fading Channels

Wanchun Liu, Daniel E. Quevedo, Karl H. Johansson, Branka Vucetic, Yonghui Li

TL;DR

A novel policy construction and analytical framework is proposed and the necessary-and-sufficient stability condition for remote state estimation of multiple linear time-invariant systems over multiple wireless time-varying communication channels is derived.

Abstract

We investigate the stability conditions for remote state estimation of multiple linear time-invariant (LTI) systems over multiple wireless time-varying communication channels. We answer the following open problem: what is the fundamental requirement on the multi-sensor-multi-channel system to guarantee the existence of a sensor scheduling policy that can stabilize the remote estimation system? We propose a novel policy construction and analytical framework and derive the necessary-and-sufficient stability condition in terms of the LTI system parameters and the channel statistics.

Stability Conditions for Remote State Estimation of Multiple Systems over Multiple Markov Fading Channels

TL;DR

A novel policy construction and analytical framework is proposed and the necessary-and-sufficient stability condition for remote state estimation of multiple linear time-invariant systems over multiple wireless time-varying communication channels is derived.

Abstract

We investigate the stability conditions for remote state estimation of multiple linear time-invariant (LTI) systems over multiple wireless time-varying communication channels. We answer the following open problem: what is the fundamental requirement on the multi-sensor-multi-channel system to guarantee the existence of a sensor scheduling policy that can stabilize the remote estimation system? We propose a novel policy construction and analytical framework and derive the necessary-and-sufficient stability condition in terms of the LTI system parameters and the channel statistics.

Paper Structure

This paper contains 21 sections, 8 theorems, 84 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Works
  4. Contributions
  5. System Model
  6. Local Estimation
  7. Markov Channel
  8. Transmission Scheduling and Remote Estimation
  9. Key Results
  10. Stability Condition
  11. Proof of Necessity
  12. Policy Construction
  13. Analysis of the Average Cost
  14. Proof of Necessity
  15. Proof of Sufficiency
  16. ...and 6 more sections

Key Result

Lemma 1

For any $\epsilon>0$, there exists $N'>0$, $\kappa >0$ and $\eta>0$ such that and

Figures (3)

  • Figure 1: The multi-sensor-multi-channel remote estimator with a single gateway. Processes, sensors, gateway and remote estimator are denoted as P$1$, P$2$, ..., P$N$, S$1$, S$2$, ..., S$N$, G and RE, respectively.
  • Figure 2: $\lambda_L$ versus $L$ over $6$ randomly generated matrix sets.
  • Figure 3: Comparison between stability conditions of Theorem \ref{['theo:main']} (solid line) and LEONG2020108759 (dashed line). The gray area denotes the parameter sets that satisfy the stability conditions.

Theorems & Definitions (17)

  • Lemma 1
  • Definition 1: Average Mean-Square Stability
  • Theorem 1
  • Remark 1: Computations
  • Corollary 1
  • proof
  • Example 1
  • Lemma 2
  • Remark 2
  • Lemma 3
  • ...and 7 more