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Canonical Form of Datatic Description in Control Systems

Guojian Zhan, Ziang Zheng, Shengbo Eben Li

TL;DR

This paper for the first time introduces the concept of canonical data form for the purpose of achieving more effective design of datatic controllers and presents two canonical data forms: temporal form and spatial form, and demonstrates their advantages in reducing instability and enhancing training efficiency in two datatic control systems.

Abstract

The design of feedback controllers is undergoing a paradigm shift from modelic (i.e., model-driven) control to datatic (i.e., data-driven) control. Canonical form of state space model is an important concept in modelic control systems, exemplified by Jordan form, controllable form and observable form, whose purpose is to facilitate system analysis and controller synthesis. In the realm of datatic control, there is a notable absence in the standardization of data-based system representation. This paper for the first time introduces the concept of canonical data form for the purpose of achieving more effective design of datatic controllers. In a control system, the data sample in canonical form consists of a transition component and an attribute component. The former encapsulates the plant dynamics at the sampling time independently, which is a tuple containing three elements: a state, an action and their corresponding next state. The latter describes one or some artificial characteristics of the current sample, whose calculation must be performed in an online manner. The attribute of each sample must adhere to two requirements: (1) causality, ensuring independence from any future samples; and (2) locality, allowing dependence on historical samples but constrained to a finite neighboring set. The purpose of adding attribute is to offer some kinds of benefits for controller design in terms of effectiveness and efficiency. To provide a more close-up illustration, we present two canonical data forms: temporal form and spatial form, and demonstrate their advantages in reducing instability and enhancing training efficiency in two datatic control systems.

Canonical Form of Datatic Description in Control Systems

TL;DR

This paper for the first time introduces the concept of canonical data form for the purpose of achieving more effective design of datatic controllers and presents two canonical data forms: temporal form and spatial form, and demonstrates their advantages in reducing instability and enhancing training efficiency in two datatic control systems.

Abstract

The design of feedback controllers is undergoing a paradigm shift from modelic (i.e., model-driven) control to datatic (i.e., data-driven) control. Canonical form of state space model is an important concept in modelic control systems, exemplified by Jordan form, controllable form and observable form, whose purpose is to facilitate system analysis and controller synthesis. In the realm of datatic control, there is a notable absence in the standardization of data-based system representation. This paper for the first time introduces the concept of canonical data form for the purpose of achieving more effective design of datatic controllers. In a control system, the data sample in canonical form consists of a transition component and an attribute component. The former encapsulates the plant dynamics at the sampling time independently, which is a tuple containing three elements: a state, an action and their corresponding next state. The latter describes one or some artificial characteristics of the current sample, whose calculation must be performed in an online manner. The attribute of each sample must adhere to two requirements: (1) causality, ensuring independence from any future samples; and (2) locality, allowing dependence on historical samples but constrained to a finite neighboring set. The purpose of adding attribute is to offer some kinds of benefits for controller design in terms of effectiveness and efficiency. To provide a more close-up illustration, we present two canonical data forms: temporal form and spatial form, and demonstrate their advantages in reducing instability and enhancing training efficiency in two datatic control systems.
Paper Structure (18 sections, 1 theorem, 12 equations, 16 figures)

This paper contains 18 sections, 1 theorem, 12 equations, 16 figures.

Table of Contents

  1. Introduction
  2. Datatic control system
  3. Canonical data form
  4. Definition of canonical data form
  5. Temporal canonical form
  6. Spatial canonical form
  7. Application
  8. Temporal canonical form
  9. Task
  10. Temporal attribute
  11. Algorithm
  12. Results
  13. Spatial canonical form
  14. Task
  15. Spatial attribute
  16. ...and 3 more sections

Key Result

Theorem 1

Consider a dataset with $n$ anchors denoted as $A_1, ..., A_n$, let $C$ be a selected sample and $S$ be any other sample. A necessary condition for $S$ in the R-neighbor area of $C$, termed as spatial filter condition, is given by where $\land$ denotes the logical AND operator.

Figures (16)

  • Figure 1: Two types of control paradigms. Modelic control (on the upper path) first fit a model with system identification and then use this model to synthesize controllers. Datatic control (on the lower path) directly solves controllers using data.
  • Figure 2: Definition of canonical data form.
  • Figure 3: Definition of temporal canonical data form.
  • Figure 4: Illustration of temporal canonical data form.
  • Figure 5: Definition of spatial canonical data form.
  • ...and 11 more figures

Theorems & Definitions (2)

  • Theorem 1: Spatial filter condition
  • proof