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In this paper, the control problem of prescribed-time adaptive neural stabilization for a class of non-strict feedback stochastic high-order nonlinear systems with dynamic uncertainty and unknown time-varying powers is discussed. The parameter separation technique, dynamic surface control technique, and dynamic signals were used to eradicate the influences of unknown time-varying powers together with state and input unmodeled dynamics, and to mitigate the computational intricacy of the backstepping. In a non-strict feedback framework, the radial basis function neural networks (RBFNNs) and Young's inequality were deployed to reconstruct the continuous unknown nonlinear functions. Finally, by establishing a new criterion of stochastic prescribed-time stability and introducing a proper bounded control gain function, an adaptive neural prescribed-time state-feedback controller was designed, ensuring that all signals of the closed-loop system were semi-global practical prescribed-time stable in probability. A numerical example and a practical example successfully validated the productivity and superiority of the control scheme.

Walking as a unique biometric tool conveys important information for emotion recognition. Individuals in different emotional states exhibit distinct walking patterns. For this purpose, this paper proposes a novel approach to recognizing emotion during walking using electroencephalogram (EEG) and inertial signals. Accurate recognition of emotion is achieved by training in an end-to-end deep learning fashion and taking into account multi-modal fusion. Subjects wear virtual reality head-mounted display (VR-HMD) equipment to immerse in strong emotions during walking. VR environment shows excellent imitation and experience ability, which plays an important role in awakening and changing emotions. In addition, the multi-modal signals acquired from EEG and inertial sensors are separately represented as virtual emotion images by discrete wavelet transform (DWT). These serve as input to the attention-based convolutional neural network (CNN) fusion model. The designed network structure is simple and lightweight while integrating the channel attention mechanism to extract and enhance features. To effectively improve the performance of the recognition system, the proposed decision fusion algorithm combines Critic method and majority voting strategy to determine the weight values that affect the final decision results. An investigation is made on the effect of diverse mother wavelet types and wavelet decomposition levels on model performance which indicates that the 2.2-order reverse biorthogonal (rbio2.2) wavelet with two-level decomposition has the best recognition performance. Comparative experiment results show that the proposed method outperforms other existing state-of-the-art works with an accuracy of 98.73%.

In this paper, the voltage and frequency regulation of microgrid with unknown disturbances and non-linear dynamics was studied. The disturbance observer was designed and the sliding mode control (SMC) method was used to realize the secondary regulation of voltage and frequency. First, a distributed secondary control protocol was designed to reduce the communication burden between generators and to solve voltage and frequency deviations. Second, a consensus protocol for secondary control of voltage and frequency was designed, based on the idea of multi-agent consensus, to indirectly ensure that the voltage and frequency to be adjusted reach the reference values when the consensus is realized. In addition, considering unknown disturbances in the microgrid, a sliding mode control strategy, based on a disturbance observer, was designed to overcome the influence of disturbances and to reduce chatter. This SMC scheme ensured finite time accessibility of the sliding mode surface. This design provides sufficient conditions for voltage and frequency regulation. The effectiveness of this design scheme was verified through simulation.

With the rapid growth of the Internet, a wealth of movie resources are readily available on the major search engines. Still, it is unlikely that users will be able to find precisely the movies they are more interested in any time soon. Traditional recommendation algorithms, such as collaborative filtering recommendation algorithms only use the user’s rating information of the movie, without using the attribute information of the user and the movie, which has the problem of inaccurate recommendations. In order to achieve personalized accurate movie recommendations, a movie recommendation algorithm based on a multi-feature attention mechanism with deep neural networks and convolutional neural networks is proposed. In order to make the predicted movie ratings more accurate, user attribute information and movie attribute information are added, user network and movie network are presented to learn user features and movie features, respectively, and a feature attention mechanism is proposed so that different parts contribute differently to movie ratings. Text features are also extracted using convolutional neural networks, in which an attention mechanism is added to make the extracted text features more accurate, and finally, personalized movie accurate recommendations are achieved. The experimental results verify the effectiveness of the algorithm. The user attribute features and movie attribute features have a good effect on the rating, the feature attention mechanism makes the features distinguish the degree of importance to the rating, and the convolutional neural network adding the attention mechanism makes the extracted text features more effective and achieves high accuracy in MSE, MAE, MAPE, R2, and RMSE indexes.

A less-complex semi-globally practical finite-time stability (SGPFS) result is presented for thyristor-controlled series compensation (TCSC) model of the power system by using dynamic surface control (DSC), H∞ control and prescribed performance control (PPC) in this paper. Meanwhile, a set of preassigned finite-time functions (PFTF) are chosen. The designed controller makes the rotor angle converge to a predefined arbitrary small area within a finite-time interval and other states of the closed-loop system are bounded. In addition, the proposed design method is simpler and the presented result is also easier to be achieved. Finally, simulation results are given to verify the effectiveness and superiority of the theoretical finding.

This paper investigates the stability of a class of quaternion-valued neural networks (QVNNs) with discrete and distributed delays. By decomposing the QVNN and forming an equivalent real-valued vector-matrix differential equation (RVVDE), based on the Lyapunov theory and some matrix inequalities, some sufficient conditions are derived to ensure the existence and uniqueness, the globally exponential stability and the globally power stability of the equilibrium of RVVDE. These conditions also apply to the QVNN. Two numerical examples are given to show the advantage and the effectiveness of the main results.

Finite-time synchronization (FTS) of uncertain fractional-order memristive neural networks (FMNNs) with leakage and discrete delays is studied in this paper, in which the impacts of uncertain parameters as well as external disturbances are considered. First, the fractional-order adaptive terminal sliding mode control scheme (FATSMC) is designed, which can effectively estimate the upper bounds of unknown external disturbances. Second, the FTS of the master–slave FMNNs is realized and the corresponding synchronization criteria and the explicit expression of the settling time (ST) are obtained. Finally, a numerical example and a secure communication application are provided to demonstrate the validity of the obtained results.

Abstract This paper investigates a gene expression model, which is mediated by sRNAs (small RNAs) and includes discrete and distributed delays. We take both the strong and weak kernel forms of distributed delay into consideration. The discrete time delay is chosen as the bifurcation parameter. By analyzing the distribution of characteristic values, we obtain the sufficient conditions of stability and examine the existence of periodic oscillations. When the discrete time delay is small and not greater than the threshold, the equilibrium of the gene expression model is asymptotically stable. When the bifurcation parameter exceeds the critical value, the model can produce limit cycles. Finally, numerical simulations are implemented to verify the correctness of our theoretical results.

This paper investigated observer-based controller for a class of singular nonlinear systems with state and exogenous disturbance-dependent noise. A new sufficient condition for finite-time stochastic input-to-state stability (FTSISS) of stochastic nonlinear systems is developed. Based on the sufficient condition, a sufficient condition on impulse-free and FTSISS for corresponding closed-loop error systems is provided. A linear matrix inequality condition, which can calculate the gains of the observer and state-feedback controller, is developed. Finally, two simulation examples are employed to demonstrate the effectiveness of the proposed approaches.

Many previous studies have indicated that pinning control and adaptive feedback control are two of most effective strategies for achieving synchronization. In this paper, we present a mixed method integrating the two control strategies to realize cluster synchronization in delayed networks with directed couplings. Based on Lyapunov stability theory and matrix theory, several criteria on cluster synchronization are obtained. Compared with the previous results on cluster synchronization, the obtained criteria can be applied to delayed network with non-identical nodes, directed couplings, and time-varying coupling strength. Finally, numerical simulations are performed to verify the theoretical results.

An underactuated horizontal spring-coupled two-link manipulator (UHSTM) is a nonlinear system that has one actuator and two degrees of freedom (DOF). This paper analyzes the nonlinear dynamics and develops a new global stabilization control method for this 2-DOF underactuated system. First, a set of suitable state variables are constructed to change the UHSTM system into a cascade nonlinear system. Second, a Lyapunov function is constructed based on the structural characteristics of the cascade system. A control law is designed to ensure the closed-loop control system to be Lyapunov stable. After that, the global asymptotical stability conditions are derived from the analysis of the closed-loop control system. Finally, numerical examples demonstrate the validity of the theoretical analysis results.

In this paper, the finite-time stabilization and destabilization of a class of quaternion-valued neural networks (QVNNs) with discrete delays are investigated. In order to surmount the difficulty of noncommutativity of quaternion, a new vector matrix differential equation (VMDE) is proposed by employing decomposition method. And then, a nonlinear controller is designed to stabilize the VMDE in a finite-time interval. Furthermore, under that controller, the finite-time stability and instability of the QVNNs are analyzed via Lyapunov function approach, and two criteria are derived, respectively; furthermore, the settling time is also estimated. At last, by two illustrative examples we verify the correctness of the conclusions.

There are many behaviors with spatio-temporal characteristics in nature. Complex spatiotemporal networks (CSNs)-based on partial differential equations are to process such issues. This paper studies two synchronization boundary control methods. An adaptive boundary controller is first studied to ensure synchronization of the CSNs. Furthermore, a pinning adaptive boundary controller is proposed to achieve synchronization of the CSNs. Two sufficient criteria of synchronization and pinning synchronization are respectively obtained. Finally, two numerical examples demonstrate the effectiveness of the proposed theoretical results.

This paper studies boundary control for exponential stabilization for a distributed parameter system, modeled by semi-linear parabolic partial integro-differential equations (PIDEs) in a 1-D spatial domain. A boundary controller based on boundary measurement is designed for exponential stabilization of the PIDE system, and it is implemented by controlling and measuring only one endpoint of the 1-D spatial domain. With the Lyapunov direct method and Wirtinger's inequality, a sufficient condition for exponential stabilization of the PIDE system with a given decay rate is investigated. Dealing with a special case of PIDE systems, one lemma called Yang inequality is proposed, and a new less conservative sufficient condition is investigated. An example with two cases is given to show the effectiveness and less conservativeness of the proposed methods by using Yang inequality.

This paper investigates the dynamic properties of a differential equation model of mammals’ circadian rhythms, including parameter identification, adaptive control, and outer synchronization. The circadian oscillator network is described by a Goodwin oscillator network, the couplings of which are from vasoactive intestinal polypeptides described by modified Van der Pol oscillators. We build up a drive-response system consisting of two networks with unknown parameters and disturbances. Then, we propose effective parameter updating laws to identify the unknown parameters and design adaptive control strategies to achieve outer synchronization in the drive-response system. As special cases, two succinct corollaries are presented for different instances. All the theoretical results are proved through strict mathematical deduction based on Lyapunov stability theory, and a numerical example is also carried out to illustrate the effectiveness.

We investigate cluster-delay synchronization of a directed network possessing cluster structures by designing an intermittent control protocol. Based on Lyapunov stability theory, we proved that synchronization can be realized for oscillators in the same cluster and cluster-delay synchronization can be realized for the whole network. By simplifying the obtained sufficient conditions, we carry out a succinct and utilitarian corollary. In addition, comparative researches are carried out to show the differences and the usefulness of the obtained results with respect to other similar controllers from the recent literature. Finally we provide two numerical examples to show the effectiveness of the control schemes.

This paper addresses the problem of projective exponential synchronization for a class of complex spatiotemporal networks with multiple time delays satisfying the homogeneous Neumann boundary conditions, where the network is modeled by coupled partial differential-difference equations (PDDEs). A distributed proportional-spatial derivative (P-sD) controller is designed by employing Lyapunov’s direct method and Kronecker product. The controller ensures the projective exponential synchronization of the PDDE network. The main result of this paper is presented in terms of standard linear matrix inequality (LMI). A numerical example is provided to show the effectiveness of the proposed design method.

This paper concerns the optimal reinforcement game problem between two opposing forces in military conflicts. With some moderate assumptions, we employ Lanchester equation and differential game theory to develop a corresponding optimization game model. After that, we establish the optimum condition for the differential game problem and give an algorithm to obtain the optimal reinforcement strategies. Furthermore, we also discuss the convergence of the algorithm. Finally, a numerical example illustrates the effectiveness of the presented optimal schemes. Our proposed results provide a theoretical guide for both making warfare command decision and assessing military actions.

This paper addresses the problem of robust H∞ control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robust H∞ P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed H∞ performance of disturbance attenuation. Moreover, a suboptimal H∞ controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN) equation, and the achieved simulation results show its effectiveness.

This paper proposes two Cucker-Smale-type flocking models by introducing both cohesive and repulsive forces to second-order multiagent systems. Under some mild conditions on the initial state of the flocking system, it is shown that the velocity consensus of the agents can be reached independent of the parameter which describes the decay of communication rates. In particular, the collision between any two agents can always be avoided by designing an appropriate bounded repulsive function based on the initial energy of the flock. Numerical examples are given to demonstrate the effectiveness of the theoretical analysis.

A class of polynomial differential systems with high-order nilpotent critical points are investigated in this paper. Those systems could be changed into systems with an element critical point. The center conditions and bifurcation of limit cycles could be obtained by classical methods. Finally, an example was given; with the help of computer algebra system MATHEMATICA, the first 5 Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 5 small amplitude limit cycles created from the high-order nilpotent critical point is also proved.

This paper considers the complete synchronization problem for coupled chaotic systems with ring connections. First, we use a direct design method to design a synchronization controller. It transforms the error system into a stable system with special antisymmetric structure. And then, we get some simple stability criteria of achieving the complete synchronization. These criteria are not only easily verified but also improve and generalize previous known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical analysis.