Stability analysis of fuzzy controllers through the computation of the Lyapunov Exponent

Autor: Leonardo Alonso Martínez Rivera, Omar López Ortega, Omar Arturo Domínguez Ramírez
Jazyk: Spanish; Castilian
Rok vydání: 2015
Předmět:
Zdroj: Revista Iberoamericana de Automática e Informática Industrial RIAI, Vol 12, Iss 4, Pp 446-456 (2015)
Druh dokumentu: article
ISSN: 1697-7912
1697-7920
DOI: 10.1016/j.riai.2015.09.006
Popis: In order to design and implement any type of controller, their stability analysis is pivotal. At this regard, Lyapunov's analytical method consists in finding a candidate function as a sufficient but not necessary condition to validate the stability of the controller. In the case of fuzzy controllers such a candidate function is not always found, leading to an uncertainty about their stability. To overcome this problem, we propose to employ the Lyapunov Exponent in order to determine whether fuzzy controllers are stable. The Lyapunov exponent is calculated through a numerical method on the time series obtained experimentally by having the fuzzy controller in closed loop with the plant dynamics. In this paper, the plant is the inverted pendulum, which is a benchmark plant to test complex control laws. Sixteen experiments were carried by modifying the rule base structure of Mamdani fuzzy controllers, which were also tested under normal and disturbed conditions. In all the cases, the Lyapunov Exponent is negative, indicating that the analyzed Mamdani controllers are indeed dissipative systems. Future applications on adaptive control are presented because the Lyapunov serves as a quantitative metric to determine controllers’ performance.
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