Output Reachable Set Analysis for Periodic Positive Systems

In this study, we use the union of the bounding hyperpyramids to estimate the output reachable set for periodic positive systems under two classes of exogenous disturbances. Optimization algorithms are used to obtain the smallest bounding hyperpyramids possible. Finally, numerical examples are given to verify the theoretical results.

Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations

In this paper, the mixed performance and reachable set of uncertain discrete systems with slow variation interval time-varying delay are considered. The original uncertain discrete systems with interval time-varying delay are first transformed into a switched system. Then, the proposed improved results are used to guarantee the stability and reachable set of the uncertain system with slow variation interval time-varying delay. The mixed performance (H2/H∞) can be derived in the same formulation simultaneously. The design scheme of robust switched control is also developed in this paper. The gains of the controller can be designed and switched to achieve stabilization and mixed performance of the system according to the delay value. Some comparisons with published results are made to show the main contribution of the proposed approach. Finally, some numerical examples are illustrated to show the main results.

Influence Maximization Algorithm Based on Reverse Reachable Set

Most of the existing influence maximization algorithms are not suitable for large-scale social networks due to their high time complexity or limited influence propagation range. Therefore, a D-RIS (dynamic-reverse reachable set) influence maximization algorithm is proposed based on the independent cascade model and combined with the reverse reachable set sampling. Under the premise that the influence propagation function satisfies monotonicity and submodularity, the D-RIS algorithm uses an automatic debugging method to determine the critical value of the number of reverse reachable sets, which not only obtains a better influence propagation range but also greatly reduces the time complexity. The experimental results on the two real datasets of Slashdot and Epinions show that D-RIS algorithm is close to the CELF (cost-effective lazy-forward) algorithm and higher than RIS algorithm, HighDegree algorithm, LIR algorithm, and pBmH (population-based metaheuristics) algorithm in influence propagation range. At the same time, it is significantly better than the CELF algorithm and RIS algorithm in running time, which indicates that D-RIS algorithm is more suitable for large-scale social network.