Adaptive fixed/predefined-time control to synchronize discontinuous multiple delay neural networks (DMDNNs) under unknown parameters identification is studied in this paper. To overcome the influence under uncertain factors in the DMDNNs, adaptive control technology is introduced into the design of controllers. In order to identify unknown parameters for state dependent switching in the DMDNNs within a fixed/predefined settling time, a fixed/predefined time identification method is derived. Under the premise that fixed time synchronization (FTS) is implemented in DMDNNs, adaptive fixed time identifier and controller are redesigned to achieve synchronization and identify unknown parameters in the DMDNNs within a predefined settling time. By the Lyapunov stability method, the corresponding synchronization criteria under FTS and predefined-time synchronization (PTS) are derived. FTS/PTS and identification of parameters under DMDNNs have potential applications in secure communication, pattern recognition, and other fields.

This paper mainly focuses on fixed time control for interlayer synchronism problem under voltage-flux–time (VFT) delay deplux memristive neural networks (DDMNNs). Distinct from most previously reported achievements, continuous memristive VFT neural networks (MMNs) field with$2^{2{n^{2}} + n}$variables are considered, where the memristor is considered as a continuous time-varying uncertain parameter, and n is the number of states in DDMNNs. This memristor is a type of continuous system built on the HP memristor. To synchronize VFT DDMNNs, a fixed time control policy is proposed for interlayer synchronism of flux and voltage values under the VFT DDMNNs. According to the second method of Lyapunov, selecting appropriate Lyapunov functionals and using inequality techniques, the structure and parameters of a kind of fixed time controller are designed, and interlayer synchronism criteria for DDMNNs are obtained. Finally, a secure communication scheme based on interlayer synchronism is designed. It is found that the fixed settling time is relative to the constructive of DDMNNs and the parameters of the fixed time controller. Note to Practitioners—This work solves the fixed time interlayer synchronism control problem of VFT DDMNNs, which can be applied to some practical scenarios, such as information security communication and image encryption. When transmitting signals in computer networks, for security, encryption mechanisms are usually added to network communication protocols to achieve secure communication. In some encryption applications, there are special requirements for speed of encryption and decryption, which requires reducing encryption and decryption time and improving efficiency of encryption. This work provides a fixed time control strategy which can achieve synchrony for VFT DDMNNs under controllable time, thereby achieving encryption under controllable time. Meanwhile, improve encryption efficiency in secure communication.

This paper mainly concentrates on the issue of fixed-time cluster secure synchronization upon interlayer switching networks with DoS attacks, in which the DoS attacks may cause random damage to the nodes/edges in networks and then generate impulsive disturbances. To resist the attacks, one robust fixed-time discontinuous control strategy is proposed, such that all the nodes in interlayer switching networks can achieve the cluster secure synchronization even when the communication topology are disconnected or changed over time after being influenced by attacks. By using the Lyapunov method, several effective conditions for fixed-time cluster secure synchronization and the maximum convergence time near to the actual value are obtained. In view of the comparison principle, a suitable estimation method upon stability time for the switching networks is established, and the stability time is computable and controllable. Moreover, the correlation among attack intensity, connectivity network, impulsive interval, impulsive disturbance intensity and synchronization time is revealed. Simulation case is finally supplied to manifest the availability of the obtained outcomes.