Novel fuzzy logic controllers with self-tuning capability

Two controllers which extend the PD+I fuzzy logic controller to deal with the plant having time varying nonlinear dynamics are proposed. The adaptation ability of the first self tuning PD+I fuzzy logic controller (STPD+I_31) is achieved by adjusting the output scaling factor automatically thereby contributing to significant improvement in performance. Second controller (STPD+I_9) is the simplified version of STPD+I_31 which is designed under the imposed constraint that allows only minimum number of rules in the rule bases. The proposed controllers are compared with two classical nonlinear controllers: the pole placement self tuning PID controller and sliding mode controller. All the controllers are applied to the two-links revolute robot for the tracking control. The tracking performance of STPD+I_31 and STPD+I_9 are much better than the pole placement self tuning PID controller during high speed motions while the performance are comparable at low and medium speed. In addition, STPD+I_31 and STPD+I_9 outperform sliding mode controller using same method of comparison study

Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices

Let \orig{A} be any matrix and let $A$ be a slight random perturbation of \orig{A}. We prove that it is unlikely that $A$ has large condition number. Using this result, we prove it is unlikely that $A$ has large growth factor under Gaussian elimination without pivoting. By combining these results, we bound the smoothed precision needed by Gaussian elimination without pivoting. Our results improve the average-case analysis of Gaussian elimination without pivoting performed by Yeung and Chan (SIAM J. Matrix Anal. Appl., 1997).Comment: corrected some minor mistake

Robust computation of linear models by convex relaxation

Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER, that can reliably fit a low-dimensional model to this type of data. This approach parameterizes linear subspaces using orthogonal projectors, and it uses a relaxation of the set of orthogonal projectors to reach the convex formulation. The paper provides an efficient algorithm for solving the REAPER problem, and it documents numerical experiments which confirm that REAPER can dependably find linear structure in synthetic and natural data. In addition, when the inliers lie near a low-dimensional subspace, there is a rigorous theory that describes when REAPER can approximate this subspace.Comment: Formerly titled "Robust computation of linear models, or How to find a needle in a haystack

Collective Influence of Multiple Spreaders Evaluated by Tracing Real Information Flow in Large-Scale Social Networks

Identifying the most influential spreaders that maximize information flow is a central question in network theory. Recently, a scalable method called "Collective Influence (CI)" has been put forward through collective influence maximization. In contrast to heuristic methods evaluating nodes' significance separately, CI method inspects the collective influence of multiple spreaders. Despite that CI applies to the influence maximization problem in percolation model, it is still important to examine its efficacy in realistic information spreading. Here, we examine real-world information flow in various social and scientific platforms including American Physical Society, Facebook, Twitter and LiveJournal. Since empirical data cannot be directly mapped to ideal multi-source spreading, we leverage the behavioral patterns of users extracted from data to construct "virtual" information spreading processes. Our results demonstrate that the set of spreaders selected by CI can induce larger scale of information propagation. Moreover, local measures as the number of connections or citations are not necessarily the deterministic factors of nodes' importance in realistic information spreading. This result has significance for rankings scientists in scientific networks like the APS, where the commonly used number of citations can be a poor indicator of the collective influence of authors in the community.Comment: 11 pages, 4 figure