This paper presents SO-Net, a permutation invariant architecture for deep learning with orderless point clouds. The SO-Net models the spatial distribution of point cloud by building a Self-Organizing Map (SOM). Based on the SOM, SO-Net performs hierarchical feature extraction on individual points and SOM nodes, and ultimately represents the input point cloud by a single feature vector. The receptive field of the network can be systematically adjusted by conducting point-to-node k nearest neighbor search. In recognition tasks such as point cloud reconstruction, classification, object part segmentation and shape retrieval, our proposed network demonstrates performance that is similar with or better than state-of-the-art approaches. In addition, the training speed is significantly faster than existing point cloud recognition networks because of the parallelizability and simplicity of the proposed architecture. Our code is available at the project website. 1

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We study in this paper the theory and applications of a nonlinear control technique, i.e., the so-called composite nonlinear feedback control, for a class of linear systems with actuator nonlinearities. It consists of a linear feedback law and a nonlinear feedback law without any switching element. The linear feedback part is designed to yield a closed-loop system with a small damping ratio for a quick response, while at the same time not exceeding the actuator limits for the desired command input levels. The nonlinear feedback law is used to increase the damping ratio of the closed-loop system as the system output approaches the target reference to reduce the overshoot caused by the linear part. It is shown that the proposed technique is capable of beating the well-known time-optimal control in the asymptotic tracking situations. The application of such a new technique to an actual hard disk drive servo system shows that it outperforms the conventional method by more than 30%. The technique can be applied to design servo systems that deal with "point-and-shoot" fast targeting.

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