Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties

Tracking Control for Triple-Integrator and Quintuple-Integrator Systems with Single Input Using Zhang Neural Network with Time Delay Caused by Backward Finite-Divided Difference Formulas for Multiple-Order Derivatives

Tracking control for multiple-integrator systems is regarded as a fundamental problem associated with nonlinear dynamic systems in the physical and mathematical sciences, with many applications in engineering fields. In this paper, we adopt the Zhang neural network method to solve this nonlinear dynamic problem. In addition, in order to adapt to the requirements of real-world hardware implementations with higher-order precision for this problem, the multiple-order derivatives in the Zhang neural network method are estimated using backward finite-divided difference formulas with quadratic-order precision, thus producing time delays. As such, we name the proposed method the Zhang neural network method with time delay. Moreover, we present five theorems to describe the convergence property of the Zhang neural network method without time delay and the quadratic-order error pattern of the Zhang neural network method with time delay derived from the backward finite-divided difference formulas with quadratic-order precision, which specifically demonstrate the effect of the time delay. Finally, tracking controllers with quadratic-order precision for multiple-integrator systems are constructed using the Zhang neural network method with time delay, and two numerical experiments are presented to substantiate the theoretical results for the Zhang neural network methods with and without time delay.

Distributed associative memory network with memory refreshing loss

Despite recent progress in memory augmented neural network (MANN) research, associative memory networks with a single external memory still show limited performance on complex relational reasoning tasks. Especially the content-based addressable memory networks often fail to encode input data into rich enough representation for relational reasoning and this limits the relation modeling performance of MANN for long temporal sequence data. To address these problems, here we introduce a novel Distributed Associative Memory architecture (DAM) with Memory Refreshing Loss (MRL) which enhances the relation reasoning performance of MANN. Inspired by how the human brain works, our framework encodes data with distributed representation across multiple memory blocks and repeatedly refreshes the contents for enhanced memorization similar to the rehearsal process of the brain. For this procedure, we replace a single external memory with a set of multiple smaller associative memory blocks and update these sub-memory blocks simultaneously and independently for the distributed representation of input data. Moreover, we propose MRL which assists a task's target objective while learning relational information existing in data. MRL enables MANN to reinforce an association between input data and task objective by reproducing stochastically sampled input data from stored memory contents. With this procedure, MANN further enriches the stored representations with relational information. In experiments, we apply our approaches to Differential Neural Computer (DNC), which is one of the representative content-based addressing memory models and achieves the state-of-the-art performance on both memorization and relational reasoning tasks.

Memory-Event-Triggered H∞ Output Control of Neural Networks With Mixed Delays

This article investigates the problem of memory-event-triggered H∞ output feedback control for neural networks with mixed delays (discrete and distributed delays). The probability density of the communication delay among neurons is modeled as the kernel of the distributed delay. To reduce network communication burden, a novel memory-event-triggered scheme (METS) using the historical system output is introduced to choose which data should be sent to the controller. Based on a constructed Lyapunov-Krasovskii functional (LKF) with the distributed delay kernel and a generalized integral inequality, new sufficient conditions are formed by linear matrix inequalities (LMIs) for designing an event-triggered H∞ controller. Finally, experiments based on a computer and a real wireless network are executed to confirm the validity of the developed method.

Fundamentals of Synthesized Optimal Control

This paper presents a new formulation of the optimal control problem with uncertainty, in which an additive bounded function is considered as uncertainty. The purpose of the control is to ensure the achievement of terminal conditions with the optimal value of the quality functional, while the uncertainty has a limited impact on the change in the value of the functional. The article introduces the concept of feasibility of the mathematical model of the object, which is associated with the contraction property of mappings if we consider the model of the object as a one-parameter mapping. It is shown that this property is sufficient for the development of stable practical systems. To find a solution to the stated problem, which would ensure the feasibility of the system, the synthesized optimal control method is proposed. This article formulates the theoretical foundations of the synthesized optimal control. The method consists in making the control object stable relative to some point in the state space and to control the object by changing the position of the equilibrium points. The article provides evidence that this approach is insensitive to the uncertainties of the mathematical model of the object. An example of the application of the method for optimal control of a group of robots is given. A comparison of the synthesized optimal control method with the direct method on the model without disturbances and with them is presented.

Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

In this contribution, the problem of multistability control in a simple model of 3D HNNs as well as its application to biomedical image encryption is addressed. The space magnetization is justified by the coexistence of up to six disconnected attractors including both chaotic and periodic. The linear augmentation method is successfully applied to control the multistable HNNs into a monostable network. The control of the coexisting four attractors including a pair of chaotic attractors and a pair of periodic attractors is made through three crises that enable the chaotic attractors to be metamorphosed in a monostable periodic attractor. Also, the control of six coexisting attractors (with two pairs of chaotic attractors and a pair of periodic one) is made through five crises enabling all the chaotic attractors to be metamorphosed in a monostable periodic attractor. Note that this controlled HNN is obtained for higher values of the coupling strength. These interesting results are obtained using nonlinear analysis tools such as the phase portraits, bifurcations diagrams, graph of maximum Lyapunov exponent, and basins of attraction. The obtained results have been perfectly supported using the PSPICE simulation environment. Finally, a simple encryption scheme is designed jointly using the sequences of the proposed HNNs and the sequences of real/imaginary values of the Julia fractals set. The obtained cryptosystem is validated using some well-known metrics. The proposed method achieved entropy of 7.9992, NPCR of 99.6299, and encryption time of 0.21 for the 256*256 sample 1 image.