Sufficient conditions on uniform approximation of multivariate functions by general Takagi-Sugeno fuzzy systems with linear rule consequent

515 motions, which would be typical for industrial settings: i) motion along 3-D straight lines, and ii) general planar motion. The proposed conjectures were shown to be reliable via experimentation with real object surfaces that were marked with artificial circular markers. The second solution approach, for 3-D general motion, advocates the use of additional features, which are coplanar to the circular features monitored. Based on the assumption that the marked object is a rigid body, the distances from a circular feature to such additional features, though unknown a priori, can be used as invariants to solve the duality problem. Experiments also showed that these methods are effective in practice. Ill-conditioned positions do exist for all solutions proposed in this paper. However, they can be found by solving a set of linear and quadratic equations, and normally eliminated during run-time by acquiring a third image of the moving object. The solution methods outlined herein were successfully utilized within our active-vision based moving-object recognition scheme [25]. REFERENCES [1] S. D. Ma, " Conics-based stereo, motion estimation, and pose determination , " Int. Analysis of a sequence of images using point and line correspondence, " in Int. location estimation of circular features for machine vision, " IEEE Trans. An adaptive sensing system with tracking and zooming a moving object, " IEICE Trans. Adaptive image feature prediction and control for visual tracking with a hand-eye coordinated camera, " IEEE Determine the position of a robot using a single calibration object, " IEEE Int. " Real-time system for accurate three-dimensional position determination and verification, " IEEE Trans. Estimation of absolute spatial position of mobile systems by hybrid opto-electronic processor, " IEEE, Int. Accurate estimate of quadratic curves from grey-level images, " J. Comput. A new approach for the recognition and positioning of two-dimensional objects, " IEEE Trans. A versatile camera calibration technique for high-accuracy 3-D machine vision metrology using off-the-shelf TV cameras and lenses, " IEEE J. recognition using pre-marking and active vision system, " in IEEE Int. Abstract—We have constructively proved a general class of multi-input single-output Takagi–Sugeno fuzzy systems to be universal approxima-tors. The systems use any types of continuous fuzzy sets, any types of fuzzy logic AND, fuzzy rules with linear rule consequent and the generalized defuzzifier. We first prove that the TS fuzzy systems can uniformly approximate any multivariate polynomial arbitrarily well, and then prove they can uniformly approximate any multivariate …