People usually interact in groups, and such groups may appear on different platforms. For instance, people often create various group chats on messaging apps (e.g., Facebook Messenger and WhatsApp) to communicate with families, friends, or colleagues. How do we identify the same people across the two platforms based on the information about the groups? This gives rise to the hypergraph alignment problem, whose objective is to find the correspondences between the sets of nodes of two hypergraphs. In a hypergraph, a node represents a person, and each hyperedge represents a group of several people. In addition, the two sets of hyperedges in the two hypergraphs can vary significantly in scales as people may use different apps at different time periods.

Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary number of nodes, rather than just two. A large number of real-world datasets are of this form - for example, lists of recipients of emails sent from an organization, users participating in a discussion thread or subject labels tagged in an online question. However, due to complex representations and lack of adequate tools, little attention has been paid to exploring the underlying patterns in these interactions.

In this paper, a robust control scheme (RCS) for Steer-by-Wire (SbW) systems with partially known dynamics is proposed. It is shown that an SbW system can be represented by a nominal model and an unknown portion. A nominal feedback controller can then be used to stabilize the nominal model and a sliding mode compensator (SMC) is designed to remove the effects of both the unknown system dynamics and uncertain road conditions on the steering performance. For practical consideration, robust exact differentiator (RED) technique is utilized to estimate the derivatives of the position signals for controller design. It is further shown that the designed RCS is able to guarantee a robust steering performance against system and road uncertainties. The comparative experimental studies are given to verify the excellent performance of the proposed RCS for SbW systems.

A new sliding mode-based learning control scheme is developed for a class of uncertain discrete-time systems. In particular, a recursive-learning controller is designed to enforce the sliding variable vector to reach and retain in the sliding mode, and the system states are then guaranteed to asymptotically converge to zero. A recently introduced “Lipschitz-like condition” for sliding mode control systems, which describes the continuity property of uncertain systems, is further extended to the discrete-time case setting in this paper. The distinguishing features of this approach include: (i) the information about the uncertainties is not required for designing the controller, (ii) the closed-loop system exhibits a strong robustness with respect to uncertainties, and (iii) the control scheme enjoys the chattering-free characteristic. Simulation results are also given to demonstrate the effectiveness of the new control technique.