Optimal hedge-algebras-based controller: Design and application

In previous papers, we introduced a new reasoning method based on quantifying linguistic domains, established a new fuzzy control algorithm, called hedge-algebras-based controller (HAC), and applied it to solve some fuzzy control problems. The HAC does not require fuzzy sets to provide the semantics of the linguistic terms used in the fuzzy rule system rather the semantics is obtained through the semantically quantifying mappings (SQMs). It was shown that the new method is very effective, i.e. for these problems it is always able to efficiently control the process toward the stable state. In the algebraic approach, the design of an HAC leads to the determination of the parameters of SQMs, which are the fuzziness measure of primary terms and linguistic hedges occurring in the fuzzy model, and the weights of a weighted averaging operator. However, there exists another problem, namely, how one can determine the optimal parameters of the method. In the present paper, we improved the HAC's design by adding an optimal step that aims to find the optimal parameters of HAC using a genetic algorithm (GA). To show the effectiveness of the proposed method, we apply it to solve again the inverted pendulum problem and the problem of holding an object on a “hill”. The results demonstrate the good performance of the designed HAC.