2,312 publications from this institution
Before launching a real viral marketing campaign, it is needed to design a spreading scheme by simulations. Based on a categorization of spreading patterns in real world and models, we point out that the existing research (especially Yang et al. (2010) Ref. [16]) implicitly assume that if a user decides to post a received message (is activated), he/she will take the reposting action promptly (Prompt Action After Activation, or PAAA). After a careful analysis on a real dataset however, it is found that the observed time differences between action and activation exhibit a heavy-tailed distribution. A simulation model for heavy-tailed pattern is then proposed and performed. Similarities and differences of spreading processes between the heavy-tailed and PAAA patterns are analyzed. Consequently, a more practical design approach of spreading scheme for viral marketing on QQ platform is proposed. The design approach can be extended and applied to the contexts of non-heavy-tailed pattern, and viral marketing on other instant messaging platforms.
In this article, we propose and study an extension of the Chen–Lai algorithm for chaotification of discrete-time dynamical systems. The proposed method is a simple but mathematically rigorous feedback control design method that can gradually make all the Lyapunov exponents of the controlled system strictly positive for any given n-dimensional dynamical system that has a uniformly bounded Jacobian but otherwise could be originally nonchaotic or even asymptotically stable.
This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.
A modified adaptive control scheme for synchronization of an uncertain Lorenz hyperchaotic system is proposed. Based on the Lyapunov stability theory, the sufficient condition for the synchronization is analyzed and proved theoretically. With the condition derived, parameter identification and synchronization of the Lorenz hyperchaotic system with all the unknown system parameters can be achieved simultaneously. Numerical simulations are presented to illustrate the effectiveness of the proposed synchronization scheme.
The problem of robust decentralized stabilization for a class of large-scale, time delay, and uncertain impulsive dynamical systems is introduced and studied. Some explicit criteria of robust exponential stabilization in the large for such systems are established. A simple approach to designing a robust decentralized controller is presented. A numerical example is given for illustrating and interpreting the theoretical results.
A simple, yet mathematically precise and rigorous, feedback control design procedure is suggested in this paper, which can rearrange all the Lyapunov exponents of the controlled system according to the user's desire, namely, to make them positive, zero, and/or negative in any desired order, for any given n-dimensional discrete-time smooth nonlinear dynamical system that could be originally nonchaotic or even asymptotically stable. The argument used is purely algebraic and the design procedure is completely schematic, without using any approximations throughout the derivation. A numerical example is included to visualize the anticontrol.
For a singular nonlinear traveling wave system of the first class, if there exist two node points of the associated regular system in the singular straight line, then the dynamics of the solutions of the singular system will be very complex. In this paper, two representative nonlinear traveling wave system models (namely, the traveling wave system of Green–Naghdi equations and the traveling wave system of the Raman soliton model for optical metamaterials) are investigated. It is shown that, if there exist two node points of the associated regular system in the singular straight line, then the singular system has no peakon, periodic peakon and compacton solutions, but rather, it has smooth periodic wave, solitary wave and kink wave solutions.
This paper investigates the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control problem for partially unknown discrete-time nonlinear systems with external disturbances and Bernoulli model-based random packet losses in different communication channels. Based on the game theory, the computed control input and external disturbances are respectively considered as the minimizing and maximizing players for satisfying an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control performance index of the concerned networked nonlinear system. Then, a Bernoulli model-based stochastic zero-sum game is formulated and a Bernoulli model-based Hamilton-Jacobi-Isaacs equation is established. It is proven that the solutions to the developed equation results in a globally stochastically asymptotically stable closed-loop system when external disturbances are not taken into account and, if accounted, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control performance index is satisfied for all kinds of deterministic square-summable external disturbances. An adaptive/approximate dynamic programming and reinforcement leaning based data-driven value iteration algorithm is developed to approximately solve the associated equation and learn the ideal feedback policy for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control problem with guaranteed convergence. Finally, a simulation study on the proposed data-driven value iteration algorithm is provided to demonstrate its effectiveness.
No abstract is provided for this article.
Many dynamic systems and industrial control processes can be represented by a multirate sampled-data uncertain system, which consists of a continuous-time uncertain subsystem and a multirate discrete-time uncertain subsystem. The uncertainties in these systems arise from unmodeled dynamics, parameter variations, sensor noises, actuator constraints, etc. As is the common practice the sampled-data uncertain system needs to be converted to a purely continuous-time or discrete-time uncertain model, so that the well-established analysis and design methods in the continuous-time or discrete-time domain can be directly applied to the equivalent model. This paper presents a new interval multipoint Pade approximation method for converting a continuous-time (discrete-time) uncertain linear system to an equivalent discrete-time (continuous-time) uncertain model. The system matrices characterizing the state-space descriptions of the original uncertain systems are represented by interval matrices. Using the approximate uncertain models obtained based on interval analysis and multipoint Pade approximation the dynamic states of the resulting models have been shown to be able to closely match those of the original uncertain systems for a relatively longer sampling period.
