Dynamic Analysis of Hybrid Impulsive Delayed Neural Networks With Uncertainties

Multiagent Meta-Reinforcement Learning for Adaptive Multipath Routing Optimization

In this article, we investigate the routing problem of packet networks through multiagent reinforcement learning (RL), which is a very challenging topic in distributed and autonomous networked systems. In specific, the routing problem is modeled as a networked multiagent partially observable Markov decision process (MDP). Since the MDP of a network node is not only affected by its neighboring nodes' policies but also the network traffic demand, it becomes a multitask learning problem. Inspired by recent success of RL and metalearning, we propose two novel model-free multiagent RL algorithms, named multiagent proximal policy optimization (MAPPO) and multiagent metaproximal policy optimization (meta-MAPPO), to optimize the network performances under fixed and time-varying traffic demand, respectively. A practicable distributed implementation framework is designed based on the separability of exploration and exploitation in training MAPPO. Compared with the existing routing optimization policies, our simulation results demonstrate the excellent performances of the proposed algorithms.

Exponential Stability of Impulsive Timescale-Type Nonautonomous Neural Networks With Discrete Time-Varying and Infinite Distributed Delays

Global exponential stability (GES) for impulsive timescale-type nonautonomous neural networks (ITNNNs) with mixed delays is investigated in this article. Discrete time-varying and infinite distributed delays (DTVIDDs) are taken into consideration. First, an improved timescale-type Halanay inequality is proven by timescale theory. Second, several algebraic inequality criteria are demonstrated by constructing impulse-dependent functions and utilizing timescale analytical techniques. Different from the published works, the theoretical results can be applied to GES for ITNNNs and impulsive stabilization design of timescale-type nonautonomous neural networks (TNNNs) with mixed delays. The improved timescale-type Halanay inequality considers time-varying coefficients and DTVIDDs, which improves and extends some existing ones. GES criteria for ITNNNs cover the stability conditions of discrete-time nonautonomous neural networks (NNs) and continuous-time ones, and these theoretical results hold for NNs with discrete-continuous dynamics. The effectiveness of our new theoretical results is verified by two numerical examples in the end.

Dynamics Analysis and Design for a Bidirectional Super-Ring-Shaped Neural Network With n Neurons and Multiple Delays

Recently, the dynamics of delayed neural networks has always incurred the widespread concern of scholars. However, they are mostly confined to some simplified neural networks, which are only made up of a small amount of neurons. The main cause is that it is difficult to decompose and analyze generally high-dimensional characteristic matrices. In this article, for the first time, we can solve the computing issues of high-dimensional eigenmatrix by employing the formula of Coates flow graph, and the dynamics is considered for a bidirectional neural network with super-ring structure and multiple delays. Under certain circumstances, the characteristic equation of the linearized network can be transformed into the equation with integration element. By analyzing the equation, we find that the self-feedback coefficient and the delays have significant effects on the stability and Hopf bifurcation of the network. Then, we achieve some sufficient conditions of the stability and Hopf bifurcation on the network. Furthermore, the obtained conclusions are applied to design a standardized high-dimensional network with bidirectional ring structure, and the scale of the standardized high-dimensional network can be easily extended or reduced. Afterward, we propose some designing schemes to expand and reduce the dimension of the standardized high-dimensional network. Finally, the results of theories are coincident with that of experiments.

Periodicity and multi-periodicity generated by impulses control in delayed Cohen-Grossberg-type neural networks with discontinuous activations

This paper discusses the periodicity and multi-periodicity in delayed Cohen-Grossberg-type neural networks (CGNNs) possessing impulsive effects, whose activation functions possess discontinuities and are allowed to be unbounded or nonmonotonic. Based on differential inclusion and cone expansion-compression fixed-point theory of set-valued mapping, several improved criteria are given to derive the positive solution with ω-periodicity and ω-multi-periodicity for delayed CGNNs under impulsive control. These ω-periodicity/ω-multi-periodicity orbits are produced by impulses control. The analytical method and theoretical results presented in this paper are of certain significance to the design of neural network models or circuits possessing discontinuous neuron activation and impulsive effects in periodic environment.

Multistability of Delayed Hybrid Impulsive Neural Networks With Application to Associative Memories

The important topic of multistability of continuous-and discrete-time neural network (NN) models has been investigated rather extensively. Concerning the design of associative memories, multistability of delayed hybrid NNs is studied in this paper with an emphasis on the impulse effects. Arising from the spiking phenomenon in biological networks, impulsive NNs provide an efficient model for synaptic interconnections among neurons. Using state-space decomposition, the coexistence of multiple equilibria of hybrid impulsive NNs is analyzed. Multistability criteria are then established regrading delayed hybrid impulsive neurodynamics, for which both the impulse effects on the convergence rate and the basins of attraction of the equilibria are discussed. Illustrative examples are given to verify the theoretical results and demonstrate an application to the design of associative memories. It is shown by an experimental example that delayed hybrid impulsive NNs have the advantages of high storage capacity and high fault tolerance when used for associative memories.