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Design and Implementation of Hedge Algebra Controller using Recursive Semantic Values for Cart-pole System

Nhat-Minh Dzoan, Thi-Thoa Mac, Hoang-Hiep Ly, Xuan-Thuan Nguyen

Abstract

This paper presents a novel approach to designing a Hedge Algebra Controller named Hedge Algebra Controller with Recursive Semantic Values (RS-HAC). This approach incorporates several newly introduced concepts, including Semantically Quantifying Simplified Mapping (SQSM) featuring a recursive algorithm, Infinite General Semantization (IGS), and Infinite General De-semantization (IGDS). These innovations aim to enhance the optimizability, scalability, and flexibility of hedge algebra theory, allowing the design of a hedge algebra-based controller to be carried out more efficiently and straightforward. An application of stabilizing an inverted pendulum on a cart is conducted to illustrate the superiority of the proposed approach. Comparisons are made between RS-HAC and a fuzzy controller of Takagi-Sugeno type (FC), as well as a linear quadratic regulator (LQR). The results indicate that the RS-HAC surpasses the FC by up to 400\% in control efficiency and is marginally better than the LQR regarding transient time in balancing an inverted pendulum on a cart.

Design and Implementation of Hedge Algebra Controller using Recursive Semantic Values for Cart-pole System

Abstract

This paper presents a novel approach to designing a Hedge Algebra Controller named Hedge Algebra Controller with Recursive Semantic Values (RS-HAC). This approach incorporates several newly introduced concepts, including Semantically Quantifying Simplified Mapping (SQSM) featuring a recursive algorithm, Infinite General Semantization (IGS), and Infinite General De-semantization (IGDS). These innovations aim to enhance the optimizability, scalability, and flexibility of hedge algebra theory, allowing the design of a hedge algebra-based controller to be carried out more efficiently and straightforward. An application of stabilizing an inverted pendulum on a cart is conducted to illustrate the superiority of the proposed approach. Comparisons are made between RS-HAC and a fuzzy controller of Takagi-Sugeno type (FC), as well as a linear quadratic regulator (LQR). The results indicate that the RS-HAC surpasses the FC by up to 400\% in control efficiency and is marginally better than the LQR regarding transient time in balancing an inverted pendulum on a cart.

Paper Structure

This paper contains 14 sections, 8 equations, 10 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Summary of Hedge algebra theory
  3. The hedge algebra theory
  4. Hedge algebra controller structure
  5. Hedge algebra controllers with recursive semantic values
  6. Infinite general semantization/de-semantization
  7. Semantically quantifying simplified mapping
  8. The structure of RS-HAC
  9. Application example: Balancing a cart-pole
  10. Cart-pole mathematical model
  11. RS-HAC design
  12. Experimental procedure
  13. RS-HAC implementation on real cart-pole system
  14. Conclusion

Figures (10)

  • Figure 1: HAC general structure for a system with $n$ observable states and $m$ inputs. Each state is separately inferred to get its corresponding intermediate control action. Subsequently, all theses actions are weighted, then combined into $m$ final control signals. Dashed arrows represents variables in semantic domains, otherwise they are in real domains.
  • Figure 2: Infinite general semantization (IGS) plotted with different parameters.
  • Figure 3: A cart-pole system
  • Figure 4: RS-HAC structure for controlling a cart-pole. Dashed lines represent operations in semantic domains, while solid lines illustrate operations in real domains
  • Figure 8: Experiment 1 results
  • ...and 5 more figures