Exponential Stability Analysis for Delayed Semi-Markovian Recurrent Neural Networks: A Homogeneous Polynomial Approach

The combined Lyapunov functionals method for stability analysis of neutral Cohen-Grossberg neural networks with multiple delays

This research article will employ the combined Lyapunov functionals method to deal with stability analysis of a more general type of Cohen-Grossberg neural networks which simultaneously involve constant time and neutral delay parameters. By utilizing some combinations of various Lyapunov functionals, we determine novel criteria ensuring global stability of such a model of neural systems that employ Lipschitz continuous activation functions. These proposed results are totally stated independently of delay terms and they can be completely characterized by the constants parameters involved in the neural system. By making some detailed analytical comparisons between the stability results derived in this research article and the existing corresponding stability criteria obtained in the past literature, we prove that our proposed stability results lead to establishing some sets of stability conditions and these conditions may be evaluated as different alternative results to the previously reported corresponding stability criteria. A numerical example is also presented to show the applicability of the proposed stability results.

Observer-based resilient dissipativity control for discrete-time memristor-based neural networks with unbounded or bounded time-varying delays

This work focuses on the issue of observer-based resilient dissipativity control of discrete-time memristor-based neural networks (DTMBNNs) with unbounded or bounded time-varying delays. Firstly, the Luenberger observer is designed, and additionally based on the observed states, the observer-based resilient controller is proposed. An augmented system is presented by considering both the error system and the DTMBNNs with the controller. Secondly, a novel sufficient extended exponential dissipativity condition is obtained for the augmented system with unbounded time-varying delays by proposing a system solutions-based estimation approach. This method is based on system solutions and without constructing any Lyapunov-Krasovskii functionals (LKF), thereby reducing the complexity of theoretical derivation and computational workload. In addition, an algorithm is proposed to solve the nonlinear inequalities in the sufficient condition. Thirdly, the sufficient extended exponential dissipativity condition for the augmented system with bounded time-varying delays is also obtained. Finally, the effectiveness of the theoretical results is illustrated through two simulation examples.

RBF neural network-based admittance PD control for knee rehabilitation robot

Early-stage rehabilitation therapy for post-stroke patients consists of intensive and accurate training sessions. During these sessions, the therapist moves the patient’s joint within its range of motion repetitively. Patients, at this stage, often cannot control their muscles, and neurological disorders may occur and lead to undesirable movements. Thus, the therapist should train the joint gently to handle any sudden involuntary movements. Otherwise, the joint may undergo excessive torques, which may injure it. In this paper, we address this case and develop a clinical rehabilitation robotic system for training the knee joint taking into account the occurrence of these undesirable movements. The developed system has an innovative mechanism to measure interaction torques exerted by involuntary movements. Then, we introduce a new control approach consisting of an admittance controller and a proportional-derivative controller augmented by a radial basis function (PD-RBF) neural network. The PD-RBF guides the robot joint along a predefined trajectory, while the admittance part tracks any sudden interaction torques and updates the predefined trajectory accordingly. Thus, the robot trains the knee joint and once an undesirable movement occurs the robot gets along with this movement smoothly, then it gets back to the predefined trajectory. To validate the performance of the proposed admittance PD-RBF controller, we consider two controllers, an admittance adaptive sliding mode control and an admittance conventional PD one. Then, a compatarive study is conducted on these controllers via real-world experiments. The obtained results verify the efficiency of the admittance PD-RBF and prove its superiority over the other aforementioned controllers.

Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

Online Reconstruction of Complex Networks From Streaming Data

The problem of reconstructing nonlinear and complex dynamical systems from available data or time series is prominent in many fields, including engineering, physical, computer, biological, and social sciences. Many methods have been proposed to address this problem and their performance is satisfactory. However, none of them can reconstruct network structure from large-scale real-time streaming data, which leads to the failure of real-time and online analysis or control of complex systems. In this article, to overcome the limitations of current methods, we first extend the network reconstruction problem (NRP) to online settings, and then develop a follow-the-regularized-leader (FTRL)-Proximal style method to address the online complex NRP; we refer to it as Online-NR. The performance of Online-NR is validated on synthetic evolutionary game network reconstruction datasets and eight real-world networks. The experimental results demonstrate that Online-NR can effectively solve the problem of online network reconstruction with large-scale real-time streaming data. Moreover, Online-NR outperforms or matches nine state-of-the-art network reconstruction methods.

3D Input Convolutional Neural Network for SSVEP Classification in Design of Brain Computer Interface for Patient User

This research was aimed at presenting performance of 3-dimensional input convolutional neural networks for steady-state visual evoked potential classification in a wireless EEG-based brain-computer interface system. Overall performance of a brain-computer interface system depends on information transfer rate. Parameters such as signal classification accuracy rate, signal stimulator structure, and user task completion time affect information transfer rate. In this study, we used 3 types of signal classification methods that are 1-dimensional, 2-dimensional, and 3-dimensional input convolutional neural network. According to online experiment with using 3-dimensional input convolutional neural network, we reached average classification accuracy rate and average information transfer rate as 93.75% and 58.35 bit/min, respectively. This both results significantly higher than the other methods that we used in experiments. Moreover, user task completion time was reduced with using 3-dimensional input convolutional neural network. Our proposed method is novel and state-of-art model for steady-state visual evoked potential classification.

Reachable Set Estimation for Discrete-Time Markovian Jump Neural Networks With Generally Incomplete Transition Probabilities

This paper is concerned with the problem of reachable set estimation for discrete-time Markovian jump neural networks with generally incomplete transition probabilities (TPs). This kind of TP may be exactly known, merely known with lower and upper bounds, or unknown. The aim of this paper is to derive a precise reachable set description for the considered system via the Lyapunov-Krasovskii functional (LKF) approach. By constructing an augmented LKF, using an equivalent transformation method to deal with the unknown TPs and utilizing the extended reciprocally convex matrix inequality, and the free matrix weighting approach to estimate the forward difference of the constructed LKF, several sufficient conditions that guarantee the existence of an ellipsoidal reachable set are established. Finally, a numerical example with simulation results is given to demonstrate the effectiveness and superiority of the proposed results.

Stochastic Finite-Time H∞ State Estimation for Discrete-Time Semi-Markovian Jump Neural Networks With Time-Varying Delays

In this article, the finite-time H_∞ state estimation problem is addressed for a class of discrete-time neural networks with semi-Markovian jump parameters and time-varying delays. The focus is mainly on the design of a state estimator such that the constructed error system is stochastically finite-time bounded with a prescribed H_∞ performance level via finite-time Lyapunov stability theory. By constructing a delay-product-type Lyapunov functional, in which the information of time-varying delays and characteristics of activation functions are fully taken into account, and using the Jensen summation inequality, the free weighting matrix approach, and the extended reciprocally convex matrix inequality, some sufficient conditions are established in terms of linear matrix inequalities to ensure the existence of the state estimator. Finally, numerical examples with simulation results are provided to illustrate the effectiveness of our proposed results.

Resilient Observer-Based Control for Cyber-Physical Systems With Multiple Transmission Channels Under Denial-of-Service

This paper investigates the resilient control problem for cyber-physical systems (CPSs) with multiple transmission channels under denial-of-service (DoS). First, a set of partial observers is designed to estimate partial states corresponding to different channels. Second, by combining the proposed partial observers, the finite-time observer technique and a switching scheme, a modified finite-time partial observer-based controller is proposed to stabilize the system in the presence of DoS. Compared with the existing results for the CPSs with multiple transmission channels, the computational burden of designing observer-based controller is reduced, and the resilience against DoS is improved by adopting the proposed finite-time partial observers. Especially, besides stability, the proposed resilient observer-based controller also provides better disturbance rejection performance.

State-Feedback Filtering for Delayed Discrete-Time Complex-Valued Neural Networks

This article explores a new filtering problem for the class of delayed discrete-time complex-valued neural networks (CVNNs) via state-feedback control design. The novelty of this article comes from the consideration of the newly developed complex-valued reciprocal convex matrix inequality as well as the complex-valued Jensen-based summation inequalities (JSIs). By employing an appropriate Lyapunov-Krasovskii functional (LKF) and by using newly proposed complex-valued inequalities, attention is concentrated on the design of a state-feedback filter such that the associated filtering error system is asymptotically stable with prescribed filter and control gain matrices. The proposed theoretical results are presented in terms of complex-valued linear matrix inequalities (LMIs) that can be solved numerically by using the YALMIP toolbox in MATLAB software. Additionally, one numerical example is given to confirm the validity of the resulting sufficient conditions with the availability of the suitable control and filter design.

Consensus via event-triggered strategy of nonlinear multi-agent systems with Markovian switching topologies

The consensus problem via event-triggered strategy of nonlinear multi-agent systems (MASs) with Markovian switching topologies is addressed in this paper. To simplify information transmission, a distributed event-triggered mechanism (ETM) is designed. By combining the Markovian switching topologies and ETM, an appropriate consensus control protocol is presented. Considering the impact of delay on systems stability, the system model is transformed by the delay system approach. By choosing a Lyapunov-Krasovskii function and applying linear matrix inequalities technique, sufficient conditions are obtained to ensure the consensus stability with H_∞ norm bound of the MASs. A numerical simulation is given to confirm the effectiveness of the designed method.

Time-delay estimation based computed torque control with robust adaptive RBF neural network compensator for a rehabilitation exoskeleton

A new approach to gait rehabilitation task of a 12 DOF lower limb exoskeleton is proposed combining time-delay estimation (TDE) based computed torque control (CTC) and robust adaptive RBF neural networks. In addition to the conventional advantages of the CTC, TDE technique is integrated to estimate unmodeled dynamics and external disturbance. To realize more accurate tracking, a robust adaptive RBF neural networks compensator is designed to approximate and compensate TDE error. The final asymptotic stability is guaranteed with Lyapunov criteria. To validate the proposed approach, co-simulation experiments are realized using SolidWorks, SimMechanics and MATLAB/Robotics Toolbox. Compared to CTC, sliding mode based CTC and TDE based CTC, the higher performances of the proposed controller are demonstrated by co-simulation.

Finite-time and fixed-time anti-synchronization of Markovian neural networks with stochastic disturbances via switching control

This paper proposes a unified theoretical framework to study the problem of finite/fixed-time drive-response anti-synchronization for a class of Markovian stochastic neural networks. State feedback switching controllers without the sign function are designed to achieve the finite/fixed-time anti-synchronization of the addressed systems. Compared with the existing synchronization criteria, our results indicate that the controllers via the switching control without the sign function are given with less conservativeness, and the controllers without any sign function can deal with the chattering problem. By employing Lyapunov functional method and properties of the Weiner process, several finite/fixed-time synchronization criteria are presented and the corresponding settling times are calculated as well. Finally, three numerical examples are provided to illustrate the effectiveness of the theoretical results.

Extended Dissipativity Analysis for Markovian Jump Neural Networks With Time-Varying Delay via Delay-Product-Type Functionals

This paper investigates the problem of extended dissipativity for Markovian jump neural networks (MJNNs) with a time-varying delay. The objective is to derive less conservative extended dissipativity criteria for delayed MJNNs. Toward this aim, an appropriate Lyapunov-Krasovskii functional (LKF) with some improved delay-product-type terms is first constructed. Then, by employing the extended reciprocally convex matrix inequality (ERCMI) and the Wirtinger-based integral inequality to estimate the derivative of the constructed LKF, a delay-dependent extended dissipativity condition is derived for the delayed MJNNs. An improved extended dissipativity criterion is also given via the allowable delay sets method. Based on the above-mentioned results, the extended dissipativity condition of delayed NNs without Markovian jump parameters is directly derived. Finally, three numerical examples are employed to illustrate the advantages of the proposed method.