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TP13; 本文概述了随机镇定与反镇定理论的研究现状.主要回顾了一个微分方程的随机镇定与反镇定普遍理论及其发展,并围绕该理论的应用和扩展从四个方面阐述连续时间系统噪声镇定理论的当前发展概况.此外,本文还概述了离散时间系统随机镇定方面的最新进展.

This paper is concerned with the exponential H∞ filtering problem for a class of discrete-time switched neural networks with random time-varying delays based on the sojourn-probability-dependent method. Using the average dwell time approach together with the piecewise Lyapunov function technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with random time-varying delays which are characterized by introducing a Bernoulli stochastic variable. Based on the derived H∞ performance analysis results, the H∞ filter design is formulated in terms of Linear Matrix Inequalities (LMIs). Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed design procedure.

In this paper, the stability and control issues of a class of uncertain nonlinear discrete-time systems in the strict feedback form are investigated. The dead-zone input in the systems, whose property is non-symmetric and discretized, is investigated. The unknown functions in the systems are approximated by using the radial basis function neural networks （RBFNNs）. Backstepping design procedure is employed in the controller and the adaptation laws design. Lyapunov analysis method is utilized to prove the stability of the closed-loop system. A simulation example is given to illustrate the effectiveness of the proposed approach.

Accurately representing the quantity and characteristics of users＇ interest in certain topics is an important problem facing topic evolution researchers, particularly as it applies to modem online environments. Search engines can provide information retrieval for a specified topic from archived data, but fail to reflect changes in interest toward the topic over time in a structured way. This paper reviews notable research on topic evolution based on the probabilistic topic model from multiple aspects over the past decade. First, we introduce notations, terminology, and the basic topic model explored in the survey, then we summarize three categories of topic evolution based on the probabilistic topic model： the discrete time topic evolution model, the continuous time topic evolution model, and the online topic evolution model. Next, we describe applications of the topic evolution model and attempt to summarize model generalization performance evaluation and topic evolution evaluation methods, as well as providing comparative experimental results for different models. To conclude the review, we pose some open questions and discuss possible future research directions.

In this paper, the leader-following consensus for discrete-time multi-agent systems with parameter uncertainties is investigated based on the event-triggered strategy. And the parameter uncertainty is assumed to be norm-bounded. A consensus protocol is designed based on the event-triggered strategy to make the multi-agent systems achieve consensus without continuous communication among agents. Each agent only needs to observe its own state to determine its own triggering instants under the triggering function in this paper. In addition, a sufficient condition for the existence of the event-triggered consensus protocol is derived and presented in terms of the linear matrix inequality. Finally, a numerical example is given to illustrate to efficiency of the event-triggered consensus protocol proposed in this paper.

In this paper, using semi-tensor product and the vector form of Boolean logical variables, the Boolean control network （BCN） is expressed as a bilinear discrete time system about state and control variables. Based on the algebraic form, the reachability and controllability avoiding undesirable states set are discussed. The reachability and controllability discussed here are under certain constraint and tile definitions of reachability and controllability avoiding undesirable states set have practical meaning. Also, the necessary and sufficient conditions for reachability and controllability are given. At last, the control sequence that steers one state to another is constructed.

A novel self-learning optimal control method for a class of discrete-time nonlinear systems is proposed based on iteration adaptive dynamic programming（ADP）algorithm.It is proven that the iteration costate functions converge to the optimal one,and a detailed convergence analysis of the iteration ADP algorithm is given.Furthermore,echo state network（ESN）architecture is used as the approximator of the costate function for each iteration.To ensure the reliability of the ESN approximator,the ESN mean square training error is constrained in the satisfactory range.Two simulation examples are given to demonstrate that the proposed control method has a fast response speed due to the special structure and the fast training process.

In this paper, consensus problems in discrete-time multiagent systems with time-invariant delays are considered. In order to characterize the structures of communication topologies, the concept of “pre-leader-follower” decomposition is introduced. Then, a necessary and sufficient condition for state consensus is established. By this method, consensus problems in networks with a single time-delay, as well as with multiple time-delays, are studied, and some necessary and sufficient conditions for solvability of consensus problems are obtained.

The performance of detector limits the overall performance of laser ranging system. And the design of multi-hit detector is one of the feasible ways to promote the performance of detector. Currently, the segmentation method or the recursive method is commonly used to analyze the multi-hit detector model. To the best of our knowledge, this paper is the first to propose a combinatorial method to solve the multi-hit detector model from the perspective of discrete time. Then, universal formulas of total signal detection probability and the average count are deduced based on the Poisson distribution signal. Furthermore, analysis is made to figure out how the average count changes with different parameters, such as the dead time, gating time, rate intensity. As a result, for GM-APD, the multi-hit detector model is verified advantageously compared to the single-hit detector model in improving the average count theoretically. Meanwhile, a discrete step feature is presented when average count changes with dead time or the gating time, which is of great significance in gating time optimization.

This paper investigates a multi-period mean-variance portfolio selection with regime switching and uncertain exit time. The returns of assets all depend on the states of the stochastic market which are assumed to follow a discrete-time Markov chain. The authors derive the optimal strategy and the efficient frontier of the model in closed-form. Some results in the existing literature are obtained as special cases of our results.