Fractional- order T- S fuzzy predictive control based free- form Surface reconstruction

The modeling method is generally used to reconstruct the optical surface as a whole for the optical free- form surface with large gradient change. However, the reconstruction accuracy is limited that cannot meet the requirements, and the local characteristics of the surface cannot be accurately characterized. Therefore, a fast surface reconstruction method based on fractional- order T- S fuzzy predictive control is proposed by this paper. By constructing a hierarchical structure of a given data set and the method of layer- by- layer precision, the effect of global surface reconstruction is achieved, solving the problem caused by the use of local support radial basis functions. In addition, a strategy based on T- S fuzzy predictive control system is designed, and the asymptotic stability theorem of the T- S fuzzy predictive control system is proposed and proved. On this basis, the asymptotic stability of the fractional- order T- S fuzzy error system is proved, and the selection method of the gain matrix is given. The experimental results show that the proposed method is also suitable for the surface reconstruction of point cloud data with extremely uneven distribution or noise. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.