Guaranteed Cost Tracking for Uncertain Coupled Multi-agent Systems Using Consensus over a Directed Graph

This paper considers the leader-follower control problem for a linear multi-agent system with directed communication topology and linear nonidentical uncertain coupling subject to integral quadratic constraints (IQCs). A consensus-type control protocol is proposed based on each agent's states relative to its neighbors and leader's state relative to agents which observe the leader. A sufficient condition is obtained by overbounding the cost function. Based on this sufficient condition, a computational algorithm is introduced to minimize the proposed guaranteed bound on tracking performance, which yields a suboptimal bound on the system consensus control and tracking performance. The effectiveness of the proposed method is demonstrated using a simulation example.Comment: Accepted for presentation at the 2013 Australian Control conferenc

How is family support related to students' GPA scores? A longitudinal study

Previous studies of the influence of family support on college students' academic performance have yielded inconsistent results. Therefore, the present study aimed to examine the link between family support and students' university-level academic performance in a more detailed way. First, we sought to clarify how two distinct aspects of perceived family support-social support and economic support-affect college students' academic performance. Second, we sought to determine how these two aspects of family support influence not only cumulative GPA scores but also the overall trend (slope) and stability (variability) of students' GPA scores across semesters. The participants in this longitudinal study were 240 university students (62 men, 178 women). The results revealed that the level of perceived family social support was important not only as a "main effect" predictor of the magnitude and stability of the students' GPA scores across three successive semesters, but also as a factor that helped female students to succeed regardless of their level of family economic support. In general, the data suggest that family social support is more important to women's success in college than to men's

Regularized Principal Component Analysis for Spatial Data

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at $p$ locations and $n$ time points with the possibility that $p>n$. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when $p$ is large relative to $n$. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical example