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From Noise to Knowledge: System Identification with Systematic Polytope Construction via Cyclic Reformulation

Hiroshi Okajima, Shun Shirahama, Tatsunori Hayashi, Nobutomo Matsunaga

TL;DR

A novel identification algorithm is proposed that derives polytopic uncertainty models by interpreting noise-induced parameter fluctuations as intrinsic uncertainty by applying cyclic reformulation with period N to linear time-invariant systems, yielding N parameter sets with slight variations that serve as polytope vertices.

Abstract

Model-based control requires accurate mathematical models to guarantee control performance and stability. However, obtaining accurate models is challenging due to process and sensor noise. This paper proposes a novel identification algorithm that derives polytopic uncertainty models by interpreting noise-induced parameter fluctuations as intrinsic uncertainty. The method applies cyclic reformulation with period N to linear time-invariant systems, yielding N parameter sets with slight variations that serve as polytope vertices. This enables systematic polytopic model construction from a single identification experiment. Simulation results demonstrate significant improvements: the proposed method achieves higher parameter estimation accuracy and reduces prediction errors by approximately half compared to conventional approaches. The vertex count N provides systematic control over the precision of uncertainty representation.

From Noise to Knowledge: System Identification with Systematic Polytope Construction via Cyclic Reformulation

TL;DR

A novel identification algorithm is proposed that derives polytopic uncertainty models by interpreting noise-induced parameter fluctuations as intrinsic uncertainty by applying cyclic reformulation with period N to linear time-invariant systems, yielding N parameter sets with slight variations that serve as polytope vertices.

Abstract

Model-based control requires accurate mathematical models to guarantee control performance and stability. However, obtaining accurate models is challenging due to process and sensor noise. This paper proposes a novel identification algorithm that derives polytopic uncertainty models by interpreting noise-induced parameter fluctuations as intrinsic uncertainty. The method applies cyclic reformulation with period N to linear time-invariant systems, yielding N parameter sets with slight variations that serve as polytope vertices. This enables systematic polytopic model construction from a single identification experiment. Simulation results demonstrate significant improvements: the proposed method achieves higher parameter estimation accuracy and reduces prediction errors by approximately half compared to conventional approaches. The vertex count N provides systematic control over the precision of uncertainty representation.
Paper Structure (29 sections, 1 theorem, 46 equations, 6 tables)

This paper contains 29 sections, 1 theorem, 46 equations, 6 tables.

Table of Contents

  1. INTRODUCTION
  2. MATRIX POLYTOPE REPRESENTATION OF PLANTS
  3. Plant with Noise
  4. Matrix Polytope Representation
  5. Parameter Estimation Error and Polytope Model Hypothesis
  6. CYCLIC REFORMULATION FOR PERIODIC TIME-VARYING SYSTEMS
  7. System Formulation and Cyclic Structure
  8. Subspace Identification with Cycled Signals
  9. Coordinate Transformation for Cyclic Structure Recovery
  10. Parameter Extraction for Periodic Time-Varying Systems
  11. INTENTIONAL PERIODICITY INDUCTION FOR UNCERTAINTY QUANTIFICATION
  12. Systematic Uncertainty Modeling via Cyclic Reformulation
  13. Application to Linear Time-Invariant Systems
  14. Coordinate Transformation and Parameter Extraction
  15. Polytope Construction and Theoretical Analysis
  16. ...and 14 more sections

Key Result

Theorem 1

Assume that the parameters $(\check{A}_*, \check{B}_*, \check{C}_*, \check{D}_*)$ are obtained via subspace identification based on cycled signals, and that the pairs $(\check{A}_*, \check{B}_*)$ and $(\check{C}_*, \check{A}_*)$ are controllable and observable, respectively. Then, the system matrice

Theorems & Definitions (1)

  • Theorem 1