Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.

A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.

Lyapunov Conditions for Finite-Time Input-to-State Stability of Impulsive Switched Systems

Dear Editor,This letter studies finite-time input-to-state stability(FTISS)for impulsive switched systems.A set of Lyapunov-based conditions are established for guaranteeing FTISS property.When constituent modes governing continuous dynamics are FTISS and discrete dynamics involving impulses are destabilizing,the FTISS can be retained if impulsive-switching signals satisfy an average dwell-time(ADT)condition.

Set Stabilization of Large-Scale Stochastic Boolean Networks:A Distributed Control Strategy

Dear Editor,This letter deals with the set stabilization of stochastic Boolean control networks(SBCNs)by the pinning control strategy,which is to realize the full control for systems by imposing control inputs on a fraction of agents.

Novel Criteria on Finite-Time Stability of Impulsive Stochastic Nonlinear Systems

Dear Editor,This letter considers the finite-time stability(FTS)problem of generalized impulsive stochastic nonlinear systems(ISNS).By employing the stochastic Lyapunov and impulsive control approach,some novel criteria on FTS are presented,where both situations of stabilizing and destabilizing impulses are considered.Furthermore,new impulse-dependent estimation strategies of stochastic settling time(SST)are proposed.

A Data-Driven Rutting Depth Short-Time Prediction Model With Metaheuristic Optimization for Asphalt Pavements Based on RIOHTrack

Rutting of asphalt pavements is a crucial design criterion in various pavement design guides. A good road transportation base can provide security for the transportation of oil and gas in road transportation. This study attempts to develop a robust artificial intelligence model to estimate different asphalt pavements’ rutting depth clips, temperature, and load axes as primary characteristics. The experiment data were obtained from19 asphalt pavements with different crude oil sources on a 2.038km long full-scale field accelerated pavement test track(Road Track Institute, RIOHTrack) in Tongzhou, Beijing. In addition,this paper also proposes to build complex networks with different pavement rutting depths through complex network methods and the Louvain algorithm for community detection. The most critical structural elements can be selected from different asphalt pavement rutting data, and similar structural elements can be found. An extreme learning machine algorithm with residual correction(RELM) is designed and optimized using an independent adaptive particle swarm algorithm. The experimental results of the proposed method are compared with several classical machine learning algorithms, with predictions of average root mean squared error(MSE), average mean absolute error(MAE), and a verage mean absolute percentage error(MAPE) for 19 asphalt pavements reaching 1.742, 1.363, and 1.94% respectively. The experiments demonstrate that the RELM algorithm has an advantage over classical machine learning methods in dealing with non-linear problems in road engineering. Notably, the method ensures the adaptation of the simulated environment to different levels of abstraction through the cognitive analysis of the production environment parameters. It is a promising alternative method that facilitates the rapid assessment of pavement conditions and could be applied in the future to production processes in the oil and gas industry.

Distributed Adaptive Resource Allocation:An Uncertain Saddle-Point Dynamics Viewpoint

This paper addresses distributed adaptive optimal resource allocation problems over weight-balanced digraphs.By leveraging state-of-the-art adaptive coupling designs for multiagent systems,two adaptive algorithms are proposed,namely a directed-spanning-tree-based algorithm and a node-based algorithm.The benefits of these algorithms are that they require neither sufficiently small or unitary step sizes,nor global knowledge of Laplacian eigenvalues,which are widely required in the literature.It is shown that both algorithms belong to a class of uncertain saddle-point dynamics,which can be tackled by repeatedly adopting the Peter-Paul inequality in the framework of Lyapunov theory.Thanks to this new viewpoint,global asymptotic convergence of both algorithms can be proven in a unified way.The effectiveness of the proposed algorithms is validated through numerical simulations and case studies in IEEE 30-bus and 118-bus power systems.

Local Bifurcation Analysis of a Delayed Fractional-order Dynamic Model of Dual Congestion Control Algorithms

In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay,the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results.

SSL-WAEIE:Self-Supervised Learning With Weighted Auto-Encoding and Information Exchange for Infrared and Visible Image Fusion

Dear editor,Infrared and visible image fusion(IVIF)technologies are to extract complementary information from source images and generate a single fused result[1],which is widely applied in various high-level visual tasks such as segmentation and object detection[2].

SAMPLED-DATA STATE ESTIMATION FOR NEURAL NETWORKS WITH ADDITIVE TIME–VARYING DELAYS

In this paper, we consider the problem of delay-dependent stability for state estimation of neural networks with two additive time–varying delay components via sampleddata control. By constructing a suitable Lyapunov–Krasovskii functional with triple and four integral terms and by using Jensen's inequality, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities(LMIs) to ensure the asymptotic stability of the equilibrium point of the considered neural networks. Instead of the continuous measurement,the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. Due to the delay-dependent method, a significant source of conservativeness that could be further reduced lies in the calculation of the time-derivative of the Lyapunov functional. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components. Finally, numerical example is given to show the superiority of proposed method.

Automatic Segmentation for Intracoronary OCT Image Based on Convolutional Neural Network and Support Vector Machine Methods

Background Cardiovascular diseases are closely associated with atherosclerotic plaque development and rupture.Traditional medical imaging techniques such as magnetic resonance imaging(MRI)and intravascular ultrasound(IVUS)were unable to identify vulnerable plaques due to their limited resolution.Fortunately,optical coherence tomography(OCT)is an advanced intravascular imaging technique developed in recent years which has high resolution approximately 10 microns and could provide more accurate morphology of coronary plaque.In particular,it has the ability to identify plaques with fibrous cap thickness<65μm,an accepted threshold value for vulnerable plaques.However,segmentation of OCT images in clinic is still mainly performed manually by physicians which is time consuming and subjective.To overcome time consumption,several methodologies have been proposed for automatic segmentation of OCT images but most of these methods were still limited by intricate image preprocessing and expensive computation.In this research,two automatic segmentation methods for intracoronary OCT image based on support vector machine(SVM)and convolutional neural network(CNN)were performed to identify the plaque region and characterize plaque components.Methods In vivo IVUS and OCT coronary plaque data from 5 patients were acquired at Emory University with patient’s consent obtained.OCT were obtained from ILUMIEN OPTIS System(St.Jude,Minnesota,MN).The OCT catheter was traversed to the segment of interest and the catheter pullback was limited at a rate of 20 mm/sec.Following the OCT image acquisition,the IVUS catheter was traversed distally though the artery to the same coronary segment(Volcano Therapeutics,Rancho Cordova)and the catheter pullback speed was at a standard rate of 0.5 mm/sec.Seventy-seven matched IVUS and OCT slices with good image quality and lipid cores were selected for our segmentation study.Manual OCT segmentation was performed by experts and used as gold standard in the automatic segmentations.VH-IVUS was used as references and guide by the experts in the manual segmentation process.Three plaque component tissue classes were identified from OCT images in this work:lipid tissue(LT),fibrous tissue(FT)and background(BG).Procedures using two machine learning methods(CNN and SVM)were developed to segment OCT images,respectively.For CNN method,the U-Net architecture was selected due to its good performance in very different biomedical segmentation and very few annotated images.For SVM method,local binary patterns(LBPs),gray level co-occurrence matrices(GLCMs)which contains contrast,correlation,energy and homogeneity,entropy and mean value were calculated as features and assembled to feed SVM classifier.The accuracies of two segmentation methods were evaluated and compared using the OCT dataset.Segmentation accuracy is defined as the ratio of the number of pixels correctly classified over the total number of pixels.Results The overall classification accuracy based CNN method reached 95.8%,and the accuracies for LT,FT and BG were 86.8%,83.4%,and 98.2%,respectively.The overall classification accuracy based SVM was 71.9%,and per-class accuracy for LT,FT and BG was 75.4%,78.3%,and67.0%,respectively.Conclusions The two methods proposed can automatically identify plaque region and characterize plaque compositions for OCT images and potentially reduce the time spent by doctors in segmenting and evaluating coronary plaque OCT images.CNN provided better segmentation accuracies compared to those achieved by SVM.

O(t^(-β))-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control toolbox.Finally,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.

Machine Learning Model Comparison for Automatic Segmentation of Intracoronary Optical Coherence Tomography and Plaque Cap Thickness Quantification

Optical coherence tomography(OCT)is a new intravascular imaging technique with high resolution and could provide accurate morphological information for plaques in coronary arteries.However,its segmentation is still commonly performed manually by experts which is time-consuming.The aim of this study was to develop automatic techniques to characterize plaque components and quantify plaque cap thickness using 3 machine learning methods including convolutional neural network(CNN)with U-Net architecture,CNN with Fully convolutional DenseNet(FC-DenseNet)architecture and support vector machine(SVM).In vivo OCT and intravascular ultrasound(IVUS)images were acquired from two patients at Emory University with informed consent obtained.Eighteen OCT image slices which included lipid core and with acceptable image quality were selected for our study.Manual segmentation from imaging experts was used as the gold standard for model training and validation.Since OCT has limited penetration,virtual histology IVUS was combined with OCT data to improve reliability.A 3-fold cross-validation method was used for model training and validation.The overall tissue classification accuracy for the 18 slices studied(total classification database sample size was 8580096 pixels)was 96.36%and 92.72%for U-Net and FC-DenseNet,respectively.The best average prediction accuracy for lipid was 91.29%based on SVM,compared to 82.84%and 78.91%from U-Net and FC-DenseNet,respectively.The overall average accuracy(Acc)differentiating lipid and fibrous tissue were 95.58%,92.33%and 81.84%for U-Net,FC-DenseNet and SVM,respectively.The average errors of U-Net,FC-DenseNet and SVM from the 18 slices for cap thickness quantification were 8.83%,10.71%and 15.85%.The average relative errors of minimum cap thickness from 18 slices of U-Net,FC-DenseNet and SVM were 17.46%,13.06%and 22.20%,respectively.To conclude,CNN-based segmentation methods can better characterize plaque compositions and quantify plaque cap thickness on OCT images and are more likely to be used in the clinical arena.Large-scale studies are needed to further develop the methods and validate our findings.

Exponential Convergence of Primal-Dual Dynamical System for Linear Constrained Optimization

Dear editor,Primal-dual dynamics(PDD)and its variants are prominent first-order continuous-time algorithms to determine the primal and dual solutions of a constrained optimization problem(COP).Due to the simple structure,they have received widespread attention in various fields,such as distributed optimization[1],power systems[2],and wireless communication[3].In view of their wide applications,there are numerous theoretic studies on the convergence properties of PDD and its variants,including the exponential stability analysis[4]-[9].

Detection and Defense Method Against False Data Injection Attacks for Distributed Load Frequency Control System in Microgrid

In the realm of microgrid(MG),the distributed load frequency control(LFC)system has proven to be highly susceptible to the negative effects of false data injection attacks(FDIAs).Considering the significant responsibility of the distributed LFC system for maintaining frequency stability within the MG,this paper proposes a detection and defense method against unobservable FDIAs in the distributed LFC system.Firstly,the method integrates a bi-directional long short-term memory(Bi LSTM)neural network and an improved whale optimization algorithm(IWOA)into the LFC controller to detect and counteract FDIAs.Secondly,to enable the Bi LSTM neural network to proficiently detect multiple types of FDIAs with utmost precision,the model employs a historical MG dataset comprising the frequency and power variances.Finally,the IWOA is utilized to optimize the proportional-integral-derivative(PID)controller parameters to counteract the negative impacts of FDIAs.The proposed detection and defense method is validated by building the distributed LFC system in Simulink.

Consensus of cyber-physical power systems based on multi-agent systems with communication constraints

The consensus protocol of cyber-physical power systems is proposed based on fractional-order multi-agent systems with communication constraints.It aims to enable each generator to reach a time-varying common rotor angle and rotor speed.Communication constraints including event-triggered sampling and partial information transmission are considered to render the consensus protocol more realistic.The Zeno behavior is excluded during the system sampling process.A sufficient condition is derived to solve the consensus problem.The effectiveness of the proposed consensus protocol is demonstrated by a numerical example.

Stability and bifurcation analysis of a fractional-order single-gene regulatory model with delays under a novel PD^α control law

In this paper,we propose a novel fractional-order proportional-derivative(PD)strategy to achieve the control of bifurcation of a fractional-order gene regulatory model with delays.The stability theory of fractional differential equations proved that with delays,some explicit conditions for the local asymptotical stability and Hopf bifurcation are given for the controlled fractional-order genetic model.It is demonstrated that the fractional-order gene regulatory model becomes controllable by adjusting the control gain parameters.In addition,the effect of fractional-order parameter on the dynamical behaviors is shown.Finally,numerical simulations are carried out to testify the validity of the main results and the availability of the fractional-order PD controller.