𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Global stability analysis of fuzzy controllers using cell mapping methods

✍ Scribed by Joseph Levitas

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
963 KB
Volume
106
Category
Article
ISSN
0165-0114

No coin nor oath required. For personal study only.

✦ Synopsis

Linear and nonlinear stability analysis of a nonlinear fuzzy logic controller is considered. The linear analysis is carried out by Lyapunov's first method (i.e. by determination of the eigenvalues of the linearized system). The nonlinear global stability analysis is executed by a combination of two methods: simple and interpolated cell mapping. Examples of controllers with a complex dynamic behavior are presented. These include controllers with multiple solutions such as (i) stable equilibrium point and stable limit circle, (ii) five unstable equilibrium points and three stable limit circles, and (iii) examples where the linear analysis is completely insufficient and only nonlinear investigation provides desirable results. The structure of domains of attraction of stable solutions is determined. Comparison of the results obtained by the cell mapping method with those provided by direct numerical integration, are presented.

πŸ“œ SIMILAR VOLUMES

Stability analysis of neural net control
Stability analysis of neural net controllers using fuzzy neural networks
✍ Thomas Feuring; James J. Buckley; Wolfram-M. Lippe; Andreas Tenhagen πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 810 KB

Neural networks can only be trained with a crisp and finite data set. Therefore, the approximation quality of a trained network is hard to verify. So, a common way in proving stability of a trained neural net controller is to demonstrate the existence of a Lyapunov function. In this article we propo