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Approximating arrival costs in distributed moving horizon estimation: A recursive method

Xiaojie Li, Xunyuan Yin

TL;DR

The paper addresses distributed state estimation for nonlinear constrained processes by introducing a recursive arrival-cost update within a partition-based DMHE framework. It derives an analytical arrival-cost expression from a distributed full-information estimator for linear unconstrained systems, develops a linear DMHE with recursive arrival costs and a stability condition, and extends the arrival-cost design to nonlinear systems via successive linearization. The resulting nonlinear DMHE formulation integrates inter-subsystem measurements and yields a scalable, constrained estimation method that preserves stability under reasonable assumptions. Validation on a reactor-separator benchmark demonstrates improved estimation accuracy and computational efficiency over alternative DMHE schemes, highlighting the approach's suitability for large-scale process monitoring and control.

Abstract

In this paper, we present a new approach to distributed moving horizon estimation for constrained nonlinear processes. The method involves approximating the arrival costs of local estimators through a recursive framework. First, distributed full-information estimation for linear unconstrained systems is presented, which serves as the foundation for deriving the analytical expression of the arrival costs for the local estimators. Subsequently, we develop a recursive arrival cost design for linear distributed moving horizon estimation. Sufficient conditions are derived to ensure the stability of the estimation error for constrained linear systems. Next, we extend the arrival cost design derived for linear systems to account for nonlinear systems, and a partition-based constrained distributed moving horizon estimation algorithm for nonlinear systems is formulated. A benchmark chemical process is used to illustrate the effectiveness and superiority of the proposed method.

Approximating arrival costs in distributed moving horizon estimation: A recursive method

TL;DR

The paper addresses distributed state estimation for nonlinear constrained processes by introducing a recursive arrival-cost update within a partition-based DMHE framework. It derives an analytical arrival-cost expression from a distributed full-information estimator for linear unconstrained systems, develops a linear DMHE with recursive arrival costs and a stability condition, and extends the arrival-cost design to nonlinear systems via successive linearization. The resulting nonlinear DMHE formulation integrates inter-subsystem measurements and yields a scalable, constrained estimation method that preserves stability under reasonable assumptions. Validation on a reactor-separator benchmark demonstrates improved estimation accuracy and computational efficiency over alternative DMHE schemes, highlighting the approach's suitability for large-scale process monitoring and control.

Abstract

In this paper, we present a new approach to distributed moving horizon estimation for constrained nonlinear processes. The method involves approximating the arrival costs of local estimators through a recursive framework. First, distributed full-information estimation for linear unconstrained systems is presented, which serves as the foundation for deriving the analytical expression of the arrival costs for the local estimators. Subsequently, we develop a recursive arrival cost design for linear distributed moving horizon estimation. Sufficient conditions are derived to ensure the stability of the estimation error for constrained linear systems. Next, we extend the arrival cost design derived for linear systems to account for nonlinear systems, and a partition-based constrained distributed moving horizon estimation algorithm for nonlinear systems is formulated. A benchmark chemical process is used to illustrate the effectiveness and superiority of the proposed method.
Paper Structure (19 sections, 7 theorems, 96 equations, 5 figures, 2 tables, 1 algorithm)

This paper contains 19 sections, 7 theorems, 96 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. System description
  5. Problem formulation
  6. Centralized full-information estimation
  7. Distributed full-information estimation
  8. Construction of local objective functions
  9. Distributed full-information estimation formulation
  10. Distributed moving horizon estimation for linear systems
  11. Arrival costs for linear systems
  12. Stability analysis
  13. Distributed moving horizon estimation for nonlinear systems
  14. Arrival cost approximation for nonlinear systems
  15. Formulation of nonlinear MHE-based estimators
  16. ...and 4 more sections

Key Result

Lemma 1

(rawlings2012postface) Consider the following two quadratic functions: where $A$ and $B$ are positive definite matrices; a and b are two vectors of compatible dimensions. Then, it holds that where

Figures (5)

  • Figure 1: A flowchart of procedures for obtaining the arrival cost
  • Figure 2: A schematic of the reactor-separator process.
  • Figure 3: Trajectories of the actual system state and the state estimates provided by the proposed DMHE algorithm for three vessels.
  • Figure 4: Trajectories of the actual system state and the state estimates provided by the proposed DMHE algorithm and the DMHE-3 approach for three vessels.
  • Figure 5: Trajectories of the estimation error norm of the proposed proposed DMHE algorithm and the DMHE-3 approach.

Theorems & Definitions (12)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Proposition 1
  • Proof
  • Lemma 4
  • Proposition 2
  • Proof
  • Theorem 1
  • Proof
  • ...and 2 more