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Distributed Identification of Stable Large-Scale Isomorphic Nonlinear Networks Using Partial Observations

Chunhui Li, Chengpu Yu

TL;DR

A particle consensus-based expectation maximization (EM) algorithm for distributed parameter identification for large-scale multi-agent networks encounters challenges due to nonlinear dynamics and partial observations.

Abstract

Distributed parameter identification for large-scale multi-agent networks encounters challenges due to nonlinear dynamics and partial observations. Simultaneously, ensuring the stability is crucial for the robust identification of dynamic networks, especially under data and model uncertainties. To handle these challenges, this paper proposes a particle consensus-based expectation maximization (EM) algorithm. The E-step proposes a distributed particle filtering approach, using local observations from agents to yield global consensus state estimates. The M-step constructs a likelihood function with an a priori contraction-stabilization constraint for the parameter estimation of isomorphic agents. Performance analysis and simulation results of the proposed method confirm its effectiveness in identifying parameters for stable nonlinear networks.

Distributed Identification of Stable Large-Scale Isomorphic Nonlinear Networks Using Partial Observations

TL;DR

A particle consensus-based expectation maximization (EM) algorithm for distributed parameter identification for large-scale multi-agent networks encounters challenges due to nonlinear dynamics and partial observations.

Abstract

Distributed parameter identification for large-scale multi-agent networks encounters challenges due to nonlinear dynamics and partial observations. Simultaneously, ensuring the stability is crucial for the robust identification of dynamic networks, especially under data and model uncertainties. To handle these challenges, this paper proposes a particle consensus-based expectation maximization (EM) algorithm. The E-step proposes a distributed particle filtering approach, using local observations from agents to yield global consensus state estimates. The M-step constructs a likelihood function with an a priori contraction-stabilization constraint for the parameter estimation of isomorphic agents. Performance analysis and simulation results of the proposed method confirm its effectiveness in identifying parameters for stable nonlinear networks.
Paper Structure (23 sections, 54 equations, 7 figures, 4 tables, 2 algorithms)

This paper contains 23 sections, 54 equations, 7 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Setup
  3. Network Topology and Communication
  4. Network Nonlinear State Space Model
  5. Problem of Interest
  6. The EM Algorithm for Networks
  7. Distributed State Estimation Using PC-DPF Algorithm
  8. Sequential Bayesian Estimation
  9. Particle Smoothing for Individual Agents
  10. The Proposed PC-DPF Algorithm
  11. Distributed Dynamic Parameter Identification Based on EM Framework
  12. E-step: Distributed Calculation of the Likelihood Function Approximation $Q({\theta}, \theta_{k})$
  13. M-Step: Parameter Identification with Stability Constraint
  14. Particle Consensus-based Distributed Particle EM algorithm
  15. The Proposed PC-DPEM Algorithm
  16. ...and 8 more sections

Figures (7)

  • Figure 1: Local communication topology of a large-scale network. $\{\tilde{x}_j^i(t)\}_{j=1}^3$ are the local state estimation particles transmitted to agent $v$ from its predecessors, $\{\tilde{x}_v^i(t)\}$ are the local state estimation particles transmitted from agent $v$ to its successors. $\{\{u_i(t)\}_{i=1}^6, u_v(t)\}$ and $\{\{y_i(t)\}_{i=1}^6, y_v(t)\}$ are locally measurable inputs and outputs of agent $v$ respectively.
  • Figure 2: The implementation strategy for the PC-DPEM algorithm, where L-PS is a shorthand form of individual agent particle smoothing and PC-PDF is a shorthand form of particle consensus-based distributed particle filtering.
  • Figure 3: Parameter identification errors for different particle numbers.
  • Figure 4: Iteration time and number of iterations for obtaining optimal parameters under different particle number conditions.
  • Figure 5: Parameter identification errors for different conditions. (a) Four different noise conditions. (b) Different structures of unknown state interactions.
  • ...and 2 more figures