Finite-time stabilization and energy consumption estimation for delayed neural networks with bounded activation function

Tradeoff analysis between time cost and energy cost for fixed-time synchronization of discontinuous neural networks

This article focuses on the tradeoff analysis between time and energy costs for fixed-time synchronization (FXTS) of discontinuous neural networks (DNNs) with time-varying delays and mismatched parameters. First, a more comprehensive lemma is systematically established to study fixed-time stability, which is less conservative than those in most current results. Besides, theoretical proof has proven that the upper bounds of the settling time (ST) in this article are more accurate compared to existing results. Second, on the grounds of the new fixed-time stability lemma, fixed-time synchronization problem for discontinuous neural networks with time-varying delays and mismatched parameters is explored, and sufficient conditions for fixed-time synchronization are obtained. Further, the upper bounds of energy cost during the synchronization process are estimated. Third, in order to achieve a balance between time cost and energy cost, the genetic algorithm is utilized to find the satisfactory control parameter. Finally, a numerical example is provided to verify the theoretical analysis's correctness and the control mechanism's feasibility.

Resilient fixed-time stabilization of switched neural networks subjected to impulsive deception attacks

This article focuses on the resilient fixed-time stabilization of switched neural networks (SNNs) under impulsive deception attacks. A novel theorem for the fixed-time stability of impulsive systems is established by virtue of the comparison principle. Existing fixed-time stability theorems for impulsive systems assume that the impulsive strength is not greater than 1, while the proposed theorem removes this assumption. SNNs subjected to impulsive deception attacks are modeled as impulsive systems. Some sufficient criteria are derived to ensure the stabilization of SNNs in fixed time. The estimation of the upper bound for the settling time is also given. The influence of impulsive attacks on the convergence time is discussed. A numerical example and an application to Chua's circuit system are given to demonstrate the effectiveness of the theoretical results.

Fixed-time and prescribed-time synchronization of quaternion-valued neural networks: A control strategy involving Lyapunov functions

A control strategy containing Lyapunov functions is proposed in this paper. Based on this strategy, the fixed-time synchronization of a time-delay quaternion-valued neural network (QVNN) is analyzed. This strategy is extended to the prescribed-time synchronization of the QVNN. Furthermore, an improved two-step switching control strategy is also proposed based on this flexible control strategy. Compared with some existing methods, the main method of this paper is a non-decomposition one, does not contain a sign function in the controller, and has better synchronization accuracy. Two numerical examples verify the above advantages.

Comprehensive analysis of fixed-time stability and energy cost for delay neural networks

This paper focuses on comprehensive analysis of fixed-time stability and energy consumed by controller in nonlinear neural networks with time-varying delays. A sufficient condition is provided to assure fixed-time stability by developing a global composite switched controller and employing inequality techniques. Then the specific expression of the upper of energy required for achieving control is deduced. Moreover, the comprehensive analysis of the energy cost and fixed-time stability is investigated utilizing a dual-objective optimization function. It illustrates that adjusting the control parameters can make the system converge to the equilibrium point under better control state. Finally, one numerical example is presented to verify the effectiveness of the provided control scheme.

Synchronization for stochastic coupled networks with Lévy noise via event-triggered control

This paper addresses the realization of almost sure synchronization problem for a new array of stochastic networks associated with delay and Lévy noise via event-triggered control. The coupling structure of the network is governed by a continuous-time homogeneous Markov chain. The nodes in the networks communicate with each other and update their information only at discrete-time instants so that the network workload can be minimized. Under the framework of stochastic process including Markov chain and Lévy process, and the convergence theorem of non-negative semi-martingales, we show that the Markovian coupled networks can achieve the almost sure synchronization by event-triggered control methodology. The results are further extended to the directed topology, where the coupling structure can be asymmetric. Furthermore, we also proved that the Zeno behavior can be excluded under our proposed approach, indicating that our framework is practically feasible. Numerical simulations are provided to demonstrate the effectiveness of the obtained theoretical results.