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Data-based approaches to learning and control by similarity between heterogeneous systems

Chenchao Wang, Deyuan Meng

TL;DR

It is shown that, with the application of similarity-based learning control, the host system can directly accomplish the same control tasks by utilizing the successful experience provided by the guest system, without having to undergo the trial-and-error process.

Abstract

This paper proposes basic definitions of similarity and similarity indexes between admissible behaviors of heterogeneous host and guest systems and further presents a similarity-based learning control framework by exploiting the offline sampled data. By exploring helpful geometric properties of the admissible behavior and decomposing it into the subspace and offset components, the similarity indexes between two admissible behaviors are defined as the principal angles between their corresponding subspace components. By reconstructing the admissible behaviors leveraging sampled data, an efficient strategy for calculating the similarity indexes is developed, based on which a similarity-based learning control framework is proposed. It is shown that, with the application of similarity-based learning control, the host system can directly accomplish the same control tasks by utilizing the successful experience provided by the guest system, without having to undergo the trial-and-error process. All results in this paper are supported by simulation examples.

Data-based approaches to learning and control by similarity between heterogeneous systems

TL;DR

It is shown that, with the application of similarity-based learning control, the host system can directly accomplish the same control tasks by utilizing the successful experience provided by the guest system, without having to undergo the trial-and-error process.

Abstract

This paper proposes basic definitions of similarity and similarity indexes between admissible behaviors of heterogeneous host and guest systems and further presents a similarity-based learning control framework by exploiting the offline sampled data. By exploring helpful geometric properties of the admissible behavior and decomposing it into the subspace and offset components, the similarity indexes between two admissible behaviors are defined as the principal angles between their corresponding subspace components. By reconstructing the admissible behaviors leveraging sampled data, an efficient strategy for calculating the similarity indexes is developed, based on which a similarity-based learning control framework is proposed. It is shown that, with the application of similarity-based learning control, the host system can directly accomplish the same control tasks by utilizing the successful experience provided by the guest system, without having to undergo the trial-and-error process. All results in this paper are supported by simulation examples.
Paper Structure (8 sections, 5 theorems, 62 equations, 9 figures, 1 algorithm)

This paper contains 8 sections, 5 theorems, 62 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Admissible behavior and problem statement
  3. Data-based verification for similarity and similarity indexes
  4. Data-based reconstruction for admissible behaviors
  5. Similarity and similarity indexes
  6. Similarity-based learning control framework
  7. Simulation examples
  8. Conclusions

Key Result

Lemma 1

For the LTV system $\Sigma_{i,\mathbb{T}},\ i\in\{1,2\}$ with initial state $x_{i0}$, its admissible behavior $\mathcal{B}_{i,x_{i0}}$ constitutes an affine set. Moreover, let the test input $U^{Test}_i$ fulfill the test principles (eq-principle1) and (eq-principle2). Then a vector $\overline{w}_{i, where

Figures (9)

  • Figure 1: Similarity-based learning control exploiting sampled data.
  • Figure 2: Existing learning-based control strategies for seeking $w_h$.
  • Figure 3: Similarity-based learning control strategy for seeking $w_h$.
  • Figure 4: Outputs of the system $\Sigma_{1,\mathbb{T}}$ and $\Sigma_{2,\mathbb{T}}$ for reference $y_d(t)$.
  • Figure 5: Outputs of the system $\Sigma_{1,\mathbb{T}}$ and $\Sigma_{3,\mathbb{T}}$ for reference $y_d(t)$.
  • ...and 4 more figures

Theorems & Definitions (23)

  • Definition 1
  • Remark 1
  • Lemma 1
  • proof
  • Remark 2
  • Definition 2
  • Definition 3
  • Lemma 2
  • proof
  • Remark 3
  • ...and 13 more