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.