|Hierarchical Fuzzy Optimal Controller for Hamilton Energy of a Generalized Chaotic Lorenz System with Hidden Attractors
Gelareh Amirizadeh, Mahdi Yaghoobi*, and Hamid Reza Kobravi
International Journal of Control, Automation, and Systems, vol. 20, no. 9, pp.3088-3097, 2022
Abstract : In this paper, a hierarchical fuzzy optimal controller is proposed to control the Hamilton energy of a generalized chaotic Lorenz system with hidden attractors. In order to force the under-control chaotic system to approach a specific desired Hamilton energy level, a fuzzy controller is designed and optimized with the genetic algorithm. In practice, the system is requested to be in a specific desired energy level in each specific situation. The controller needs to be tuned separately for every new desired energy level; however, this is not an optimal approach. Here, a new hierarchical scheme is proposed, in which, the lower-level fuzzy controller is optimized for a few numbers of desired levels, and an upper-level fuzzy system is designed to adjust the fuzzy controller parameters based on the trained optimal ones, taking the desired energy level into account. The proposed hierarchical fuzzy optimal control scheme is applied to the generalized chaotic Lorenz system that shows sufficient performance.
Keyword : Generalized Lorenz system, Hamilton energy, hidden attractors, hierarchical fuzzy controller.