Interval type-2 generalized fuzzy hyperbolic modelling and control of nonlinear systems

Abstract

Generalized Fuzzy Hyperbolic Models (GFHMs) offer a simpler structure and less computational complexity than the typical fuzzy systems. Type-2 fuzzy systems, in contrast, have better handling of uncertainty but at the cost of higher computational complexity. Here, we propose a synergistic hybrid framework of interval type-2 fuzzy systems and GFHMs for a better uncertainty handling and simpler computational structure in the modelling and control of nonlinear systems. For this purpose, we first extend the GFHM to a computational model with various width and subsequently propose interval type-2 generalized fuzzy hyperbolic systems (IT2-GFHS) as a computational framework for nonlinear systems modelling. We then employ this IT2-GFHS in a general sliding-based robust nonlinear controller. Theoretical Lyapunov analysis reveals the overall asymptotic stability of the resulting closed-loop system. The numerical simulations for system modelling and identification on two nonlinear benchmark problems also reveal higher accuracy, lower computation time, and fewer adjustable parameters for the proposed IT2-GFHS models. Furthermore, applications to two nonlinear benchmark control problems show similar performance in terms of robustness to noise and disturbances compared with type-2 fuzzy systems, with the IT2-GFHS-based nonlinear controller having considerably fewer computations and floating-point operations. Finally, the proposed approach is experimentally implemented to control a 3-Prismatic-Series-Prismatic (3-PSP) parallel robot. Experimental results also confirm the improved tracking performance of the proposed method compared with interval type-2 and type-1 fuzzy systems, while also requiring fewer adjustable parameters.