New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

Abstract

This article addresses the problems of fixed-time stabilization for a class of quaternion fuzzy neural networks (QFNNs) with time-varying delay. The QFNNs are developed by dividing our system into four real-valued parts based on the Hamilton rule. Then, based on fixed-time stability theory, some inequality techniques, and selecting the appropriate controllers and Lyapunov function, a novel criterion guaranteeing the fixed-time stabilization and the finite-time stabilization of the addressed system is derived. Finally, three numerical examples are presented to show the effectiveness of our theoretical results. K E Y W O R D S finite-time stabilization, fixed-time stabilization, fuzzy neural networks, quaternion neural networks, time-varying delay

Event‐triggered H∞$$ {H}_{\infty } $$ state estimation for neural networks with time‐varying delays: The continuous‐time case

“…Along the closed loop trajectory for system (5) with the H ∞ performance, the derivatives of the functions in ( 16) are…”

“…(i) Different from AFBII, it is easy to deal with the right-hand side of inequality (8) as the reciprocal convex property is transformed to a convex property. (ii) By multiplying time-varying delay with matrices, it yields delay-product-type matrices such as d(t)MR In this article, our objective is to present an event-triggered H ∞ performance state estimation criterion for estimation error system (5). The H ∞ state estimation problem is to find a stable state estimator in the form (4) for a prescribed scalar 𝛾, such that ||e(t)|| 2 < 𝛾||w(t)|| 2 (11) for all nonzero w(t) ∈  2 [0, ∞).…”

“…The manifestation of time delays in neurons may cause oscillation, instability, or would significantly debilitate the performance of the NNs. Thus, the research on delayed NNs (DNNs) is always a hot topic 4,5 …”

“…Thus, the research on delayed NNs (DNNs) is always a hot topic. 4,5 With the rapid development of digital technologies, networked control systems (NCSs) have also received extensive attention. In order to reduce the waste of computing resources, it is very important to choose the appropriate sampling strategy in the process of signal digitization.…”

Fixed/Preassigned-Time Synchronization of Fuzzy Memristive Fully Quaternion-Valued Neural Networks Based on Event-Triggered Control

“…The exponential synchronization for QVMNNs with time-varying delayed were addressed in [16,17]. Moreover, the issues of synchronization associated with quaternion-valued fuzzy neural networks have been reported in [18][19][20]. Nevertheless, due to the complexity of quaternion-valued and memristor-based neurons, there are fewer related references on quaternion-valued fuzzy memristive neural networks (QVFMNNs).…”