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Moving horizon partition-based state estimation of large-scale systems -- Revised version

Marcello Farina, Giancarlo Ferrari-Trecate, Riccardo Scattolini

TL;DR

This paper develops three distributed state-estimation schemes, PMHE1, PMHE2, and PMHE3, for large-scale linear systems partitioned into non-overlapping subsystems. Each subsystem runs a reduced-order Moving Horizon Estimator over a horizon $N$, sharing varying levels of state estimates and covariance information according to two communication models, and enforcing state constraints via tailored cost terms and LMIs. The authors provide convergence conditions, including Schur stability criteria for the error dynamics and simpler partition-quality bounds, and discuss offline design to ensure bounded covariances. The work balances decentralization, communication load, and estimation accuracy, offering practical PMHE options for scalable networked systems like power grids or transport networks, with explicit procedures for online implementation and convergence guarantees.

Abstract

This report presents three Moving Horizon Estimation (MHE) methods for discrete-time partitioned linear systems, i.e. systems decomposed into coupled subsystems with non-overlapping states. The MHE approach is used due to its capability of exploiting physical constraints on states in the estimation process. In the proposed algorithms, each subsystem solves reduced-order MHE problems to estimate its own state and different estimators have different computational complexity, accuracy and transmission requirements among subsystems. In all cases, conditions for the convergence of the estimation error to zero are analyzed.

Moving horizon partition-based state estimation of large-scale systems -- Revised version

TL;DR

This paper develops three distributed state-estimation schemes, PMHE1, PMHE2, and PMHE3, for large-scale linear systems partitioned into non-overlapping subsystems. Each subsystem runs a reduced-order Moving Horizon Estimator over a horizon , sharing varying levels of state estimates and covariance information according to two communication models, and enforcing state constraints via tailored cost terms and LMIs. The authors provide convergence conditions, including Schur stability criteria for the error dynamics and simpler partition-quality bounds, and discuss offline design to ensure bounded covariances. The work balances decentralization, communication load, and estimation accuracy, offering practical PMHE options for scalable networked systems like power grids or transport networks, with explicit procedures for online implementation and convergence guarantees.

Abstract

This report presents three Moving Horizon Estimation (MHE) methods for discrete-time partitioned linear systems, i.e. systems decomposed into coupled subsystems with non-overlapping states. The MHE approach is used due to its capability of exploiting physical constraints on states in the estimation process. In the proposed algorithms, each subsystem solves reduced-order MHE problems to estimate its own state and different estimators have different computational complexity, accuracy and transmission requirements among subsystems. In all cases, conditions for the convergence of the estimation error to zero are analyzed.
Paper Structure (15 sections, 17 theorems, 141 equations)

This paper contains 15 sections, 17 theorems, 141 equations.

Table of Contents

  1. Introduction
  2. Partitioned systems
  3. Three moving horizon partition-based algorithms
  4. Models for estimation and transmission of information
  5. The PMHE estimation problems
  6. Choice of the weights $Q_{k/t-1}^{[i]}$ and $R_{k/t-1}^{[i]}$ for PMHE1 and PMHE2
  7. Computation of $\Pi_{t-N/t-1}^{[i]}$ for PMHE1 and PMHE2
  8. Update of $\Pi_{t-N/t-1}^{[i]}$ for PMHE1
  9. Update of $\Pi_{t-N/t-1}^{[i]}$ for PMHE2
  10. Convergence properties of the proposed estimators
  11. Simpler conditions for PMHE2 and PMHE3 and a measure of the quality of the partition
  12. Algorithmic summary for PMHE1
  13. Discussion and conclusions
  14. Optimization
  15. Proofs

Key Result

Lemma 1

Assume that the noise covariances are chosen as in point (II) of Section sec:QeR-proc. Then, a sufficient condition for lmi:PMHE1 to hold is that the matrix is positive semidefinite, where $\otimes$ denotes the Kronecker product operator. In this case lmi:PMHE1 is fulfilled by the update lmi:Kalman_UP1.

Theorems & Definitions (19)

  • Lemma 1
  • Definition 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Theorem 1
  • Theorem 2
  • Lemma 5
  • Corollary 1
  • Lemma 6
  • ...and 9 more