A delay-dividing approach to robust stability of uncertain stochastic complex-valued Hopfield delayed neural networks

In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a delay-dividing approach is devised to study the robust stability issue of uncertain neural networks. Specifically, the uncertain stochastic complex-valued Hopfield neural network (USCVHNN) with time delay is investigated. Here, the uncertainties of the system parameters are norm-bounded. Based on the Lyapunov mathematical approach and homeomorphism principle, the sufficient conditions for the global asymptotic stability of USCVHNN are derived. To perform this derivation, we divide a complex-valued neural network (CVNN) into two parts, namely real and imaginary, using the delay-dividing approach. All the criteria are expressed by exploiting the linear matrix inequalities (LMIs). Based on two examples, we obtain good theoretical results that ascertain the usefulness of the proposed delay-dividing approach for the USCVHNN model

Stochastic memristive quaternion-valued neural networks with time delays: An analysis on mean square exponential input-to-state stability

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying Itoˆ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results

Sustainable Supply Chain System for Defective Products with Different Carbon Emission Strategies

Many nations have created ecological policies and regulations to prevent industries from emitting excessive amounts of carbon emissions into the environment. While significant progress has been achieved in the direction of sustainable growth, many nations still rely on nonrenewable energy sources. This study explores the viability of investing in green technology to achieve the optimal decisions (lot sizes, lead time, and green investment amount) in a two-echelon supply chain system by considering human error with two carbon emission strategies: carbon taxes and limited carbon emissions. It entails the inspection of every shipped lot by the buyer to identify defective products that could have resulted from the vendor’s production process. We show a constrained non-linear program and design a calculus-optimization technique to solve it. The methodology used in this research is the quantitative method, which is based on the principles of operations research, and the models are built on mathematically oriented inventory theory. The results imply that an outsized ecological carbon footprint can be reduced without compromising customer service by designing optimal inventory strategies. The findings also confirm that green investment is the greatest economical method for reducing carbon emissions and system costs

A Sustainable Production Scheduling with Backorders under Different Forms of Rework Process and Green Investment

Rework is currently a necessity for businesses and commercial organizations across the world. It is only beneficial in tackling climate change if the process emits less greenhouse gases than would otherwise be emitted. This study designs an optimal production scheduling model to reduce both carbon emissions during the processes of production, transport and storage, and setup cost by leveraging on green technology efforts in an imperfect production process where a fraction of items is erroneous so that the firm may run out of inventory. The producer implements a rework strategy to rectify the flawed products, anda flexible rework rate is offered since the rework might be executed on various schemes. The flexible rework allows the producer to choose therework rate, which can differ from the production rate, as well as the rework process itself, which can be asynchronous or synchronous.The two forms of green investments: quadratic and exponential are considered in the study. The main point of the study is to derive a solution procedure of the various problem settings associated with the rework rate, rework process and green investment. The findings suggest that developing the optimal production schedule (lot-sizes, backorders, setup cost and green investment amount) can lower the manufacturing sector’s excessive ecological carbon emissions. The findings also support the idea that making green investments is the most cost-effective way to cut carbon emissions and setup cost simultaneously

A Sustainable Production Scheduling with Backorders under Different Forms of Rework Process and Green Investment

Rework is currently a necessity for businesses and commercial organizations across the world. It is only beneficial in tackling climate change if the process emits less greenhouse gases than would otherwise be emitted. This study designs an optimal production scheduling model to reduce both carbon emissions during the processes of production, transport and storage, and setup cost by leveraging on green technology efforts in an imperfect production process where a fraction of items is erroneous so that the firm may run out of inventory. The producer implements a rework strategy to rectify the flawed products, anda flexible rework rate is offered since the rework might be executed on various schemes. The flexible rework allows the producer to choose therework rate, which can differ from the production rate, as well as the rework process itself, which can be asynchronous or synchronous.The two forms of green investments: quadratic and exponential are considered in the study. The main point of the study is to derive a solution procedure of the various problem settings associated with the rework rate, rework process and green investment. The findings suggest that developing the optimal production schedule (lot-sizes, backorders, setup cost and green investment amount) can lower the manufacturing sector’s excessive ecological carbon emissions. The findings also support the idea that making green investments is the most cost-effective way to cut carbon emissions and setup cost simultaneously

An extended analysis on robust dissipativity of uncertain stochastic generalized neural networks with markovian jumping parameters

The main focus of this research is on a comprehensive analysis of robust dissipativity issues pertaining to a class of uncertain stochastic generalized neural network (USGNN) models in the presence of time-varying delays and Markovian jumping parameters (MJPs). In real-world environments, most practical systems are subject to uncertainties. As a result, we take the norm-bounded parameter uncertainties, as well as stochastic disturbances into consideration in our study. To address the task, we formulate the appropriate Lyapunov–Krasovskii functional (LKF), and through the use of effective integral inequalities, simplified linear matrix inequality (LMI) based sufficient conditions are derived. We validate the feasible solutions through numerical examples using MATLAB software. The simulation results are analyzed and discussed, which positively indicate the feasibility and effectiveness of the obtained theoretical findings

Global Stability Analysis of Neural Networks with Constant Time Delay via Frobenius Norm

This paper deals with the global asymptotic robust stability (GARS) of neural networks (NNs) with constant time delay via Frobenius norm. The Frobenius norm result has been utilized to find a new sufficient condition for the existence, uniqueness, and GARS of equilibrium point of the NNs. Some suitable Lyapunov functional and the slope bounded functions have been employed to find the new sufficient condition for GARS of NNs. Finally, we give some comparative study of numerical examples for explaining the advantageous of the proposed result along with the existing GARS results in terms of network parameters