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Combining Learning and Control in Linear Systems

Andreas A. Malikopoulos

TL;DR

This framework allows us to combine offline model-based control with online learning approaches and thus circumvent current challenges in deriving optimal control strategies in applications where a large volume of data is added to the system gradually in real time and not altogether in advance.

Abstract

In this paper, we provide a theoretical framework that separates the control and learning tasks in a linear system. This separation allows us to combine offline model-based control with online learning approaches and thus circumvent current challenges in deriving optimal control strategies in applications where a large volume of data is added to the system gradually in real time and not altogether in advance. We provide an analytical example to illustrate the framework.

Combining Learning and Control in Linear Systems

TL;DR

This framework allows us to combine offline model-based control with online learning approaches and thus circumvent current challenges in deriving optimal control strategies in applications where a large volume of data is added to the system gradually in real time and not altogether in advance.

Abstract

In this paper, we provide a theoretical framework that separates the control and learning tasks in a linear system. This separation allows us to combine offline model-based control with online learning approaches and thus circumvent current challenges in deriving optimal control strategies in applications where a large volume of data is added to the system gradually in real time and not altogether in advance. We provide an analytical example to illustrate the framework.
Paper Structure (9 sections, 3 theorems, 36 equations, 1 figure)

This paper contains 9 sections, 3 theorems, 36 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Notation
  4. Modeling Framework
  5. Separating Learning and Control Tasks
  6. Illustrative Example
  7. Optimal Control Strategy
  8. Solution Through Separation Between Learning and Control
  9. Concluding Remarks

Key Result

Theorem 1

The information state $\Pi_{t}(Y_{0:t}, U_{0:t-1})(X_{t},\hat{X}_t)$ does not depend on the control strategy $\textbf{g}\in\mathcal{G}$. Furthermore, there exists a function $\phi_t$ such that for all $t=0,1,\ldots, T-1.$

Figures (1)

  • Figure 1: The proposed framework on separating learning and control, where the separated control strategy is applied to both the actual system and the system's model in parallel.

Theorems & Definitions (8)

  • Definition 1
  • Theorem 1
  • Definition 2
  • Proposition 1
  • proof
  • Remark 1
  • Theorem 2
  • proof