A time-optimal aircraft-following model is introduced to address air traffic flow interference by velocity reduction. The objective function is set up as minimizing the recovery time during which the separation minima are not infringed and the separation of the air traffic flow returns to the initial separation at the terminal time. Pontryagin’s minimum principle is used to solve the optimum aircraft-following velocity control law. An analytical minimum safe following separation is also provided under the time-optimal control law. The simulation results show that the precision first-order tracking accuracy is achieved without losing the separation.
Point of interest (POI) recommendation problem in location based social network (LBSN) is of great importance and the challenge lies in the data sparsity, implicit user feedback and personalized preference. To improve the precision of recommendation, a tensor decomposition based collaborative filtering (TDCF) algorithm is proposed for POI recommendation. Tensor decomposition algorithm is utilized to fill the missing values in tensor (user-category-time). Specifically, locations are replaced by location categories to reduce dimension in the first phase, which effectively solves the problem of data sparsity. In the second phase, we get the preference rating of users to POIs based on time and user similarity computation and hypertext induced topic search (HITS) algorithm with spatial constraints, respectively. Finally the user’s preference score of locations are determined by two items with different weights, and the Top-N locations are the recommendation results for a user to visit at a given time. Experimental results on two LBSN datasets demonstrate that the proposed model gets much higher precision and recall value than the other three recommendation methods.
