Yurong Liu

In this paper, we design novel high order probabilistic numerical algorithms for forward backward stochastic differential equations. Moreover, we derive the error estimates and prove the high order convergence rates of the proposed schemes. Because the proposed scheme involves conditional expectations, an estimator based on the multilevel Monte Carlo method is applied to approximate the conditional expectations. Furthermore, we theoretically demonstrate that the computational complexity of our numerical method is proportional to the square of prescribed accuracy. Numerical experiments are given to illustrate the theoretical results.

Large-scale Internet of Things (IoT) systems are characterized by massive numbers of interconnected devices, heterogeneous dynamics, and complex interaction structures, which can be effectively modeled using complex networks. In many IoT applications, secure cluster synchronization is essential for coordinated and reliable operation, yet it is highly vulnerable to cyber-attacks, particularly replay attacks that maliciously reuse previously transmitted but valid data. This paper investigates the secure cluster synchronization problem for discrete-time nonlinear complex networks representing IoT systems under stochastic replay attacks. A probabilistic replay attack model with bounded consecutive attack duration is introduced to capture the random and intermittent characteristics of realistic attack behaviors. To mitigate the adverse impact of replayed information, a PID-based cluster synchronization control strategy is developed, where proportional, integral, and derivative actions are jointly exploited to enhance robustness against outdated and compromised signals. By constructing an appropriate Lyapunov functional and employing stochastic analysis techniques, sufficient conditions are derived to guarantee asymptotic mean-square cluster synchronization. A systematic controller synthesis procedure is further provided. Numerical simulations demonstrate the effectiveness and improved resilience of the proposed approach compared with conventional proportional control schemes.

In this article, the encoding-decoding-based state estimation problem is investigated for a class of continuous-time nonlinear complex networks (CNs) subject to communication bandwidth constraints. Based on the sampled outputs from a subset of network nodes, a novel dynamic event-driven encoding mechanism is integrated into the design of state estimator, where a time-varying auxiliary parameter is utilized to modulate the triggering condition in a dynamical fashion, enabling the event detector to decide whether the data packet should be released at the periodic sampling instants. Specifically, when the dynamic triggering condition is satisfied, the data are first encoded into a codeword and subsequently transmitted to the estimator through a digital communication channel. The Zeno behavior can be naturally prevented due to the periodic feature of the proposed event detector. By leveraging the Lyapunov theory and the matrix inequality techniques, sufficient conditions are established to ensure the exponential stability of the estimation error system. In addition, a convex optimization approach is employed to design the estimator gain with the goal of maximizing the allowable bound of the sampling intervals. Finally, an illustrative example and a practical example involving a three-area power system are provided to showcase the effectiveness of the proposed state estimation method.