在复杂网络理论研究中，由于分数阶微积分的记忆性及遗传性，分数阶神经网络逐渐兴起并发展为该领域的研究热点。分数阶时变时滞神经网络的伪状态估计在其应用过程中具有重要的支撑作用和参考价值，是分数阶神经网络理论的一个基本问题。基于事件触发机制，本项目拟针对分数阶时变时滞神经网络的伪状态估计问题展开研究：1）构造新型分数阶Lyapunov-Krasovskii（L-K）泛函，为分数阶L-K泛函的构造提供数学思路，丰富分数阶Lyapunov稳定性理论；2）证明新型分数阶微分不等式，并用于分数阶L-K泛函的分数阶导数的估计，为分数阶系统的理论分析提供数学技巧；3）设计分数阶事件触发条件，构造Arcak型时滞相关的分数阶非脆弱伪状态观测器，获得分数阶时变时滞神经网络伪状态估计的判别条件。预期成果将丰富分数阶时变时滞神经网络的伪状态估计理论，为其在人工智能、控制工程等领域中的应用提供理论指导和科学依据。

Fractional order neural networks have gradually emerged and developed into a research hotspot due to fractional calculus’s memorability and heredity in the study of complex network theory. Pseudo state estimation as a basic problem has important theoretical supports to applications of fractional order neural networks with time-varying delays. Based on the event-triggered mechanism, this project will study the pseudo state estimation of fractional order time-varying delayed neural networks. 1) Some new fractional order Lyapunov-Krasovskii (L-K) functionals will be constructed to provide mathematical ideas for fractional order L-K functionals and enrich the fractional order Lyapunov’s stability theory. 2) Proving some novel fractional order differential inequalities which can be used to estimate the fractional order derivative of the fractional order L-K functionals and provide mathematical skills for the theoretical analysis of fractional order systems. 3) Fractional order event-triggering conditions and fractional order Arcak type non-fragile pseudo state observers will be designed, based on which some discriminant conditions for the pseudo state estimation of fractional order time-varying delayed neural networks will be obtained. The expected results will enrich the pseudo state estimation theory of fractional order time-varying delayed neural networks and provide theoretical guidance and scientific basis for their applications in artificial intelligence and control engineering.