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In this article, an adaptive neural safe tracking control scheme is studied for a class of uncertain nonlinear systems with output constraints and unknown external disturbances. To allow the output to stay in the desired output constraints, a boundary protection approach is developed and utilized in the output constrained problem. Since the generated output constraint trajectory is piecewise differentiable, a dynamic surface method is utilized to handle it. For the purpose of approximating the system uncertainties, a radial basis function neural network (RBFNN) is adopted. Under the output of the RBFNN, the disturbance observer technology is employed to estimate the unknown compound disturbances of the system. Finally, the Lyapunov function method is utilized to analyze the convergence of the tracking error. Taking a two-link manipulator system, as an example, the simulation results are presented to illustrate the feasibility of the proposed control scheme.

Generalized eigenvector plays an essential role in the signal processing field. In this paper, we present a novel neural network learning algorithm for estimating the generalized eigenvector of a Hermitian matrix pencil. Differently from some traditional algorithms, which need to select the proper values of learning rates before using, the proposed algorithm does not need a learning rate and is very suitable for real applications. Through analyzing all of the equilibrium points, it is proven that if and only if the weight vector of the neural network is equal to the generalized eigenvector corresponding to the largest generalized eigenvalue of a Hermitian matrix pencil, the proposed algorithm reaches to convergence status. By using the deterministic discrete-time method, some convergence conditions, which can be satisfied with probability 1, are also obtained to guarantee its convergence. Simulation results show that the proposed algorithm has a fast convergence speed and good numerical stability. The real application demonstrates its effectiveness in tracking the optimal vector of beamforming.

Human-on-the-loop (HOTL) system is regarded as a promising technology to allow autonomous underwater vehicle (AUV) to track the most adequate target point as soon as possible. However, the unique characteristics of the underwater environment make it challenging to perform the tracking task. This article is concerned with a finite-time tracking control issue for AUV, subjected to unavailable velocity signals in the measurement side and uncertain model parameters in physical side. A HOTL system, including operator, buoys, AUV and sensors, is first provided to construct a cooperative tracking network. For such system, operator in surface control center decides the tracking mission based on all available data. Then, a buoy-assisted localization estimator is utilized by AUV to acquire its position, through which a fast terminal sliding mode observer is developed to estimate the velocity of AUV in finite time. With the estimated velocity information, an adaptive-nonsingular fast terminal sliding mode tracking controller is designed to drive AUV to the target point in finite time. For the proposed velocity observer and tracking controller, the signum and differential functions are employed together to improve the convergence speed and reduce the chattering. Besides that, the proposed solution can not only guarantee finite-time velocity observation, but also achieve finite-time tracking control. Finally, simulation and experimental results are both presented to verify the effectiveness.

The tethered formation system has been widely studied due to its extensive use in aerospace engineering, such as Earth observation, orbital location, and deep space exploration. The deployment of such a multitethered system is a problem because of the oscillations and complex formation maintenance caused by the space tether's elasticity and flexibility. In this article, a triangle tethered formation system is modeled, and an exact stable condition for the system's maintaining is carefully analyzed, which is given as the desired trajectories; then, a new control scheme is designed for its spinning deployment and stable maintenance. In the proposed scheme, a novel second-order sliding mode controller is given with a designed nonsingular sliding-variable. Based on the theoretical proof, the addressed sliding variable from the arbitrary initial condition can converge to the manifold in finite time, and then sliding to the equilibrium in finite time as well. The simulation results show that compared with classic second sliding-mode control, the proposed scheme can speed up the convergence of the states and sliding variables.

Power routing (PR) provides a good choice to improve the modular converter reliability by equalizing the lifetime among multi-cells. The existing PR strategies just equalize the lifetime of power semiconductor devices (PSDs) by routing lighter loads for aged cells. However, the neglect of capacitor may mislead the multi-cell lifetime convergence. Besides, the light load allocation of the aging cell does not always mean the lifetime extension considering topologies and operation principles. Hence, this paper proposed a capacitor lifetime-based PR for input-series-output-parallel (ISOP) connected dual active bridge (DAB) converter. The proposed strategy can achieve the same accuracy as existing PR strategies, greatly reducing computation time and the complexity of the hardware circuit. Moreover, the non-monotonic relationship between the damage growth rate and load of each cell is revealed and a damage growth rate constraint is developed to ensure the PR feasibility. Simulation is performed to verify the validity of the proposed strategy and constraints. Finally, a scaled down prototype has been developed to verify the PR feasibility and obtain the non-monotonic relationship, verifying the necessity of proposed constraints. In addition, the effect of PR on the thermal stress and cumulative damage of capacitors is verified by a temperature test.

This paper focuses on the problem of prescribedtime control for a class of uncertain nonlinear systems. First, a prescribed-time stability theorem is proposed by following the adaptive technology for the first time. Based on this theorem, a new state feedback control strategy is put forward by using the backstepping method for high-order nonlinear systems with unknown parameters to ensure the prescribed-time convergence. Moreover, the prescribed-time controller is obtained in the form of continuous time-varying feedback, which can render all system states converge to zero within the prescribed-time. It should be noted that the prescribed-time is independent of system initial conditions, which means that the prescribed-time can be set arbitrarily within the physical limitations. Finally, two simulation examples are provided to illustrate the effectiveness of our proposed algorithm.

Nonlinear and nonconvex optimization problems are vital and fundamental problems in science and engineering fields. In this article, a novel finite-time circadian rhythms learning network (called FT-CRLN) is proposed for solving nonlinear and nonconvex optimization problems with periodic noises. Different from the traditional recurrent neural networks, the proposed FT-CRLN can suppress the periodic noise notably and achieve excellent convergence performance in solving nonlinear and nonconvex problems. The theoretical analysis and rigorous mathematical proof verify the superior convergence, high accuracy, and strong robustness of the proposed FT-CRLN. The simulation results demonstrate the effectiveness and robustness of the proposed FT-CRLN in solving nonlinear and nonconvex problems compared with other state-of-art neural networks.

High-dimensional data are highly correlative and redundant, making it difficult to explore and analyze. Amount of unsupervised dimensionality reduction (DR) methods has been proposed, in which constructing a neighborhood graph is the primary step of DR methods. However, there exist two problems: 1) the construction of graph is usually separate from the selection of projection direction and 2) the original data are inevitably noisy. In this article, we propose an unsupervised adaptive embedding (UAE) method for DR to solve these challenges, which is a linear graph-embedding method. First, an adaptive allocation method of neighbors is proposed to construct the affinity graph. Second, the construction of affinity graph and calculation of projection matrix are integrated together. It considers the local relationship between samples and global characteristic of high-dimensional data, in which the cleaned data matrix is originally proposed to remove noise in subspace. The relationship between our method and local preserving projections (LPPs) is also explored. Finally, an alternative iteration optimization algorithm is derived to solve our model, the convergence and computational complexity of which are also analyzed. Comprehensive experiments on synthetic and benchmark datasets illustrate the superiority of our method.

We study the rates of convergence from empirical surrogate risk minimizers to the Bayes optimal classifier. Specifically, we introduce the notion of \emph{consistency intensity} to characterize a surrogate loss function and exploit this notion to obtain the rate of convergence from an empirical surrogate risk minimizer to the Bayes optimal classifier, enabling fair comparisons of the excess risks of different surrogate risk minimizers. The main result of the paper has practical implications including (1) showing that hinge loss is superior to logistic and exponential loss in the sense that its empirical minimizer converges faster to the Bayes optimal classifier and (2) guiding to modify surrogate loss functions to accelerate the convergence to the Bayes optimal classifier., Under Minor Revision in TNNLS

This work investigates the stabilization problem of uncertain stochastic Markovian jump systems (MJSs) under communication constraints. To reduce the bandwidth usage, a discrete-time Markovian chain is employed to implement the stochastic communication protocol (SCP) scheduling of the sensor nodes, by which only one sensor node is chosen to access the network at each transmission instant. Moreover, due to the effect of amplitude attenuation, time delay, and random interference/noise, the transmission may be inevitably subject to the Rice fading phenomenon. All of these constraints make the controller only receive the fading signal from one activated sensor node at each instant. A merge approach is first used to deal with two Markovian chains; meanwhile, a compensator is designed to provide available information for the controller. By a compensator and mode-based sliding-mode controller, the resulting closed-loop system is ensured to be input-to-state stable in probability (ISSiP), and the quasisliding mode is attained. Moreover, an iteration optimizing algorithm is provided to reduce the convergence domain around the sliding surface via searching a desirable sliding gain, which constitutes an effective GA-based sliding-mode control strategy. Finally, the proposed control scheme is verified via the simulation results.

The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the addition of partial functions locally known at each node. A number of methods are available for addressing this problem, having different advantages. The goal of this work is to achieve the maximum possible convergence rate. As the first step towards this end, we propose a new method which we show converges faster than other available options. As with most distributed optimization methods, convergence rate depends on a step size parameter. As the second step towards our goal we complement the proposed method with a fully distributed method for estimating the optimal step size that maximizes convergence speed. We provide theoretical guarantees for the convergence of the resulting method in a neighborhood of the solution. Also, for the case in which the global objective function has a single local minimum, we provide a different step size selection criterion together with theoretical guarantees for convergence. We present numerical experiments showing that, when using the same step size, our method converges significantly faster than its rivals. Experiments also show that the distributed step size estimation method achieves an asymptotic convergence rate very close to the theoretical maximum.

In this article, the problem of H∞ codesign for nonlinear control systems with unmatched uncertainties and adjustable parameters is investigated. The main purpose is to solve the adjustable parameters and H∞ controller simultaneously so that better robust control performance can be achieved. By introducing a bounded function and defining a special cost function, the problem of solving the Hamilton-Jacobi-Isaacs equation is transformed into an optimization problem with nonlinear inequality constraints. Based on the sum of squares technique, a novel policy iteration algorithm is proposed to solve the problem of the H∞ codesign. Moreover, one modified algorithm for optimizing the robust performance index is given. The convergence and the performance improvement of new iteration policy algorithms are proved. Simulation results are presented to demonstrate the effectiveness of the proposed algorithms.

Mobile Deep Learning (MDL) has emerged as a privacy-preserving learning paradigm for mobile devices. This paradigm offers unique features such as privacy preservation, continual learning and low-latency inference to the building of personal mobile sensing applications. However, squeezing Deep Learning to mobile devices is extremely challenging due to resource constraint. Traditional Deep Neural Networks (DNNs) are usually over-parametered, hence incurring huge resource overhead for on-device learning. In this paper, we present a novel on-device deep learning framework named MDLdroidLite that transforms traditional DNNs into resource-efficient model structures for on-device learning. To minimize resource overhead, we propose a novel Release-and-Inhibit Control (RIC) approach based on Model Predictive Control theory to efficiently grow DNNs from tiny to backbone. We also design a gate-based fast adaptation mechanism for channel-level knowledge transformation to quickly adapt new-born neurons with existing neurons, enabling safe parameter adaptation and fast convergence for on-device training. Our evaluations show that MDLdroidLite boosts on-device training on various PMS datasets with 28x to 50x less model parameters, 4x to 10x less floating number operations than the state-of-the-art model structures while keeping the same accuracy level.

Robot path planning in 3D space is a challenging problem for its complex configuration. Sampling-based algorithms have gained great success in solving path planning problems in 3D space, but the quality of the initial path is not guaranteed and the convergence to the optimal solution is slow. To address these problems, in this article, we present a novel sampling-based path planning framework enhanced by the deep neural network (DNN) with applications to 3D space. In the proposed framework, we first train the DNN with a number of successful path planning cases in 3D space. Then the DNN is utilized to predict the promising region where the feasible path probably exists for a given path planning problem. This predicted promising region serves as a nonuniform sampling heuristic to bias the sampling process of the path planner. In this way, the path planner can focus on the promising region in the exploration and exploitation process so that the path planning speed gets accelerated. We conduct numerical simulations to evaluate the performance of the proposed algorithm and the results show that it can perform much better than conventional path planning algorithms. Furthermore, we also investigate the performance of different DNN architectures for path planning in 3D space.

Convolutional transform learning (CTL), learning filters by minimizing the data fidelity loss function in an unsupervised way, is becoming very pervasive, resulting from keeping the best of both worlds: the benefit of unsupervised learning and the success of the convolutional neural network. There have been growing interests in developing efficient CTL algorithms. However, developing a convergent and accelerated CTL algorithm with accurate representations simultaneously with proper sparsity is an open problem. This article presents a new CTL framework with a log regularizer that can not only obtain accurate representations but also yield strong sparsity. To efficiently address our nonconvex composite optimization, we propose to employ the proximal difference of the convex algorithm (PDCA) which relies on decomposing the nonconvex regularizer into the difference of two convex parts and then optimizes the convex subproblems. Furthermore, we introduce the extrapolation technology to accelerate the algorithm, leading to a fast and efficient CTL algorithm. In particular, we provide a rigorous convergence analysis for the proposed algorithm under the accelerated PDCA. The experimental results demonstrate that the proposed algorithm can converge more stably to desirable solutions with lower approximation error and simultaneously with stronger sparsity and, thus, learn filters efficiently. Meanwhile, the convergence speed is faster than the existing CTL algorithms.

In this article, through a combination of the deterministic learning (DL) method and the adaptive high gain observer (AHGO) technology, a fault identification approach for a class of nonlinear systems in canonical form is proposed. By using the DL method, the partial persistent excitation condition of the identification system is satisfied, and then, the AHGO technology is exploited to estimate the states and the neural network weights simultaneously. To analyze the convergence of the proposed method, we first analyze the uniformed completely observability (UCO) property of the linear part of the nonlinear identification system. Then, by using the Lipschitz property of the nonlinear item and the Bellman-Gronwall lemma, we show that the UCO property of the nonlinear identification system is depended on the UCO property of the linear part when the observer gain is chosen large. Therefore, by using the UCO property of the nonlinear identification system and the Lyapunov stability theorem, the convergence of the proposed learning observer is proven. The attraction of this article is based on the analysis of the UCO property of the identification system, and the convergence of the proposed learning observer can be directly proven. The simulation example is given to demonstrate the effectiveness of the proposed method.

This paper investigates a distributed competition behavior in multi-robot coordination under variable communication topology and switching one. In terms of multi-robot competition-based coordination, a winner-take-all (WTA) strategy is leveraged to address this issue with inevitable environmental barriers incorporated. Moreover, an innovative control theory stimulated gradient neural network (CTSGNN) algorithm is proposed to realize the WTA with prominent robustness and convergence over the traditional ones. Besides, to adapt to diversified local communication modes among multi-robot systems, fast variable and low switching topologies are constructed to establish two dynamic consensus estimators, accompanied by the proposed distributed control schemes. Traditional algorithms are introduced and served as a contrast. Afterward, the global convergence of the proposed algorithm in dealing with multi-robot competitive coordination, the universality of the application scenario, as well as the weaknesses of traditional methods are substantiated theoretically. The effectiveness and superiority of the proposed CTSGNN algorithm and the resultant distributed control schemes by integrating consensus estimators are further sustained via simulations.

This paper addresses the problem of robust fixed-time attitude stabilization for tilt tri-rotor unmanned aerial vehicle subjects to parameter uncertainties and external disturbances. First, a novel fixed-time stable system with a faster convergence rate is proposed. Second, a nonsingular fixed-time sliding mode surface is developed, which has better convergence performance than existing methods. Third, a continuous fast fixed-time sliding mode control law is proposed by applying the developed sliding mode surface and adaptive technique. As a result, the convergence time of the closed-loop system is bounded and independent of the initial conditions. Simulation and experiments are presented to verify that the proposed scheme can effectively and rapidly achieve attitude stabilization while maintaining high control precision and robustness.

The Tsetlin Machine (TM) is a recent machine learning algorithm with several distinct properties, such as interpretability, simplicity, and hardware-friendliness. Although numerous empirical evaluations report on its performance, the mathematical analysis of its convergence is still open. In this article, we analyze the convergence of the TM with only one clause involved for classification. More specifically, we examine two basic logical operators, namely, the "IDENTITY"- and "NOT" operators. Our analysis reveals that the TM, with just one clause, can converge correctly to the intended logical operator, learning from training data over an infinite time horizon. Besides, it can capture arbitrarily rare patterns and select the most accurate one when two candidate patterns are incompatible, by configuring a granularity parameter. The analysis of the convergence of the two basic operators lays the foundation for analyzing other logical operators. These analyses altogether, from a mathematical perspective, provide new insights on why TMs have obtained state-of-the-art performance on several pattern recognition problems., Comment: 23 pages, 10 figures

This article develops an adaptive observation-based efficient reinforcement learning (RL) approach for systems with uncertain drift dynamics. A novel concurrent learning adaptive extended observer (CL-AEO) is first designed to jointly estimate the system state and parameter. This observer has a two-time-scale structure and does not require any additional numerical techniques to calculate the state derivative information. The idea of concurrent learning (CL) is leveraged to use the recorded data, which leads to a relaxed verifiable excitation condition for the convergence of parameter estimation. Based on the estimated state and parameter provided by the CL-AEO, a simulation of experience-based RL scheme is developed to online approximate the optimal control policy. Rigorous theoretical analysis is given to show that the practical convergence of the system state to the origin and the developed policy to the ideal optimal policy can be achieved without the persistence of excitation (PE) condition. Finally, the effectiveness and superiority of the developed methodology are demonstrated via comparative simulations.

This paper reveals the power and frequency oscillation mechanism of the islanded cascaded-type virtual synchronous generators (VSGs), and proposes a decentralized mutual damping suppression method. In the proposed scheme, the mutual damping term is constructed via the decentralized manner with transmission line current. It contributes to increasing damping and accelerating the frequency convergence of cascaded-type VSGs in the dynamic process. As a result, the power and frequency oscillations are restrained, and the system dynamic performance is improved. Further, the system stability based on the Lyapunov energy function method is proved. Finally, the effectiveness of the proposed decentralized mutual damping control is verified by simulations and experimental results.

Because of COVID-19, factories are facing many difficulties, such as shortage of workers and social alienation. How to improve production performance under limited labor resources is an urgent problem for global manufacturing factories. This work studies an energy-efficient job-shop scheduling problem with limited workers. Those workers can have multiskills. A many-objective model with five objectives, that is: 1) makespan; 2) total tardiness; 3) total idle time; 4) total worker cost; and 5) total energy, is built. To solve this many-objective optimization problem (MaOP), a novel fitness evaluation mechanism (FEM) based on fuzzy correlation entropy (FCE) is adopted. Two construction methods for reference points are proposed to build the bridge between MaOP and a fuzzy set. Based on FCE and cluster methods, an environmental selection mechanism (ESM) is proposed to achieve a balance between solution convergence and diversity. With the proposed FEM and ESM, two many-objective evolutionary algorithms are proposed to solve MaOP. The effect of FCE-based FEM and ESM on the performance of algorithms is verified via experiments. The proposed algorithms are compared with four well-known peers to test their performance. The extensive experimental results show that they are very competitive for the considered many-objective scheduling problem.

The security and economy of multienergy systems (MESs) are directly threatened by the potential cyberattacks. It is of great importance to investigate the effects of cyberattacks, e.g., denial of service (DoS) attacks, on distributed energy management algorithms. To this end, this article focuses on exploring how the frequency and the time of duration of DoS attacks influence the behavior of Newton-Raphson-based distributed energy management (NRBDEM) algorithm for MES and in which condition the optimal operations can still be obtained. First, a switched NRBDEM algorithm is presented, which is composed of the normal operation mode and the attack mode. In the attack mode, the attackers are able to change the communication structure at will and make it unconnected to destroy the convergence of the switched NRBDEM algorithm. Then, by making use of automatons to generate the hybrid time domain, the switched NRBDEM algorithm is further modeled and formulated as a hybrid dynamical system, which provides a mathematical model for the subsequent convergence analysis. Therein, the generated hybrid time domain satisfies the average dwell-time constraint and time-ratio constraint to limit the persistent attacks. Furthermore, we analyze the restrained conditions for persistent attacks, under which the optimality and convergence of the switched NRBDEM algorithm can be guaranteed still. Finally, simulation results demonstrate the effectiveness of the proposed method.

In convolutional neural networks (CNNs), generating noise for the intermediate feature is a hot research topic in improving generalization. The existing methods usually regularize the CNNs by producing multiplicative noise (regularization weights), called multiplicative regularization (Multi-Reg). However, Multi-Reg methods usually focus on improving generalization but fail to jointly consider optimization, leading to unstable learning with slow convergence. Moreover, Multi-Reg methods are not flexible enough since the regularization weights are generated from a definite manual-design distribution. Besides, most popular methods are not universal enough, because these methods are only designed for the residual networks. In this article, we, for the first time, experimentally and theoretically explore the nature of generating noise in the intermediate features for popular CNNs. We demonstrate that injecting noise in the feature space can be transformed to generating noise in the input space, and these methods regularize the networks in a Mini-batch in Mini-batch (MiM) sampling manner. Based on these observations, this article further discovers that generating multiplicative noise can easily degenerate the optimization due to its high dependence on the intermediate feature. Based on these studies, we propose a novel additional regularization (Addi-Reg) method, which can adaptively produce additional noise with low dependence on intermediate feature in CNNs by employing a series of mechanisms. Particularly, these well-designed mechanisms can stabilize the learning process in training, and our Addi-Reg method can pertinently learn the noise distributions for every layer in CNNs. Extensive experiments demonstrate that the proposed Addi-Reg method is more flexible and universal, and meanwhile achieves better generalization performance with faster convergence against the state-of-the-art Multi-Reg methods.

We study decentralized non-convex finite-sum minimization problems described over a network of nodes, where each node possesses a local batch of data samples. In this context, we analyze a single-timescale randomized incremental gradient method, called GT-SAGA. GT-SAGA is computationally efficient as it evaluates one component gradient per node per iteration and achieves provably fast and robust performance by leveraging node-level variance reduction and network-level gradient tracking. For general smooth non-convex problems, we show the almost sure and mean-squared convergence of GT-SAGA to a first-order stationary point and further describe regimes of practical significance where it outperforms the existing approaches and achieves a network topology-independent iteration complexity respectively. When the global function satisfies the Polyak-Lojaciewisz condition, we show that GT-SAGA exhibits linear convergence to an optimal solution in expectation and describe regimes of practical interest where the performance is network topology-independent and improves upon the existing methods. Numerical experiments are included to highlight the main convergence aspects of GT-SAGA in non-convex settings.

This paper proposes a method for enlarging the region of attraction of Linear Model Predictive Controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the Feasibility Governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC feedback law remains feasible. Offline polyhedral projection algorithms based on multi-objective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference.

A robust finite-time control (FTC) framework using continuous terminal sliding-mode control (SMC) and high-order sliding-mode observer (HOSMO) is discussed to realize the trajectory tracking of flexible-joint robots in this article. Control performances of the robots always suffer from unknown matched and mismatched time-varying disturbances. Traditional SMC exists with a chattering phenomenon and cannot cope with mismatched time-varying disturbances due to its inherent structure property. For this reason, two HOSMOs are devised to estimate the time-varying disturbances on the link and motor side, respectively. Then, by fusing the states and disturbance estimations into a novel terminal sliding-mode surface, a continuous robust FTC scheme is developed. The proposed control strategy can not only handle both matched and mismatched time-varying disturbances but also obtain a finite-time convergence performance. The rigorous finite-time stability analysis of the closed-loop system under the proposed control method is guaranteed. The results are illustrated to verify the effectiveness and robustness of the proposed design approach.

Due to the high variability and uncertainty of the wind speed, interval forecast can provide more information for decision-makers to achieve a better energy management compared to the traditional point forecast. In this paper, a Knee-based Lower Upper Bound Estimation Method (K-LUBE) is proposed to construct wind speed prediction intervals (PIs). First, we analyze the underlying limitations of traditional direct interval forecast methods, i.e., their obtained prediction intervals often fail to achieve a good balance between the interval width and the coverage probability. K-LUBE resolves the difficulty based on a multi-objective optimization framework in conjunction with a knee selection criterion. Specifically, a PI-NSGA-II multi-objective optimization algorithm is designed to obtain a set of Pareto optimal solutions. A parameter transfer and a sample training strategies are developed to significantly improve the convergence speed of the optimization procedure. Then the knee selection criterion is introduced to select the best trade-off solution among the obtained solutions. In comparison with traditional methods, this method can always provide a reliable prediction interval for decision makers. The procedure is automatic and requires no parameter to be specified in advance, making it more practical for use. Effectiveness of the proposed K-LUBE method are demonstrated through extensive comparisons with four traditional direct interval forecast methods and four classical benchmark models.

In this paper, the finite-time and fixed-time attractiveness problems are investigated for nonlinear impulsive systems. The aim of the proposed problems is to establish some general Lyapunov theorems and settling-time estimates for finite-time and fixed-time attractiveness of nonlinear impulsive systems by analysis technics. Moreover, some comparisons with the existing results are also given. The classical finite-time and fixed-time convergence theorems for nonlinear impulse-free systems are well extended to nonlinear impulsive systems by our results. Furthermore, the existing results of finite-time and fixed-time attractiveness for nonlinear impulsive systems are well improved. Finally, some simulations are utilized to illustrate the usefulness of the theoretical analysis.

The multiple autonomous underwater vehicle (AUV) formation plays an important role in underwater missions, such as oceanographic sampling and water pollution monitoring. This article presents the mechatronic design, modeling, formation control, and experiments of multiple AUVs. The structure of the AUV and a simplified mathematical model for tracking control are described. To achieve formation control, we formulate a control framework for the multiple AUVs. The upper layer is a formation algorithm based on a novel leader-follower control law. The bottom layer is a dynamic controller based on active disturbance rejection control (ADRC). The formation algorithm is in charge of calculating reference values for the followers to maintain a desired pattern with the leader. The stability and convergence properties of the algorithm have been analyzed using the Lyapunov stability method. Meanwhile, an ADRC approach-based dynamic controller is established to track the reference values. Numerical simulations are carried out to analyze formation control and validate the control framework. The multiple AUVs can switch and maintain the formation between the one-line pattern and the V pattern. Finally, extensive formation field experiments involving the one-line pattern and the V pattern show the good motion ability of the self-designed AUVs and also verify the feasibility of the proposed control approach.

A non-negative latent factor (NLF) model with a single latent factor-dependent, non-negative and multiplicative update (SLF-NMU) algorithm is frequently adopted to extract useful knowledge from non-negative data represented by high-dimensional and sparse (HiDS) matrices arising from various service applications. However, its convergence rate is rather slow. To address this issue, this study proposes a Generalized Nesterov's acceleration-incorporated, Non-negative and Adaptive Latent Factor (GNALF) model. It results from a) incorporating a generalized Nesterov's accelerated gradient (NAG) method into an SLF-NMU algorithm, thereby achieving an NAG-incorporated and element-oriented non-negative (NEN) algorithm to perform efficient parameter update; and b) making its regularization and acceleration hyper-parameters self-adaptive via incorporating the principle of a particle swarm optimization algorithm into the training process, thereby implementing a highly adaptive and practical model. Empirical studies on six large sparse matrices from different recommendation service applications show that a GNALF model achieves very high convergence rate without the need of hyper-parameter tuning, making its computational efficiency significantly higher than state-of-the-art models. Meanwhile, such efficiency gain does not result in accuracy loss, since its prediction accuracy is comparable with its peers. Hence, it can better serve practical service applications with real-time demands.

As an effective application form for large-scale and efficient use of distributed power, microgrid not only realizes the flexible control of distributed power, but also provides reliable power supply for the load. However, the power quality on the load side will be severely deteriorated when the microgrid is disturbed. To cope with this issue, an improve linear active disturbance rejection control (LADRC) technique is proposed in this paper. In this technology, the idea of series correction is introduced into the disturbance observation channel of linear extended state observer (LESO). This strategy can achieve more accurate tracking of disturbance items through the correction link (CL), and handle the unknown modeling error and external disturbances of the system as an overall disturbance through a single structure. Then according to the linear feedback law to achieve good control of the output-side converter. Moreover, the traceability, convergence and stability of ILADRC are analyzed. More importantly, guidance on parameters configuration is given on the basis of performance analysis. Finally, the validity of the proposed improved LADRC technique is verified on a 40-kW experiment platform.

This article investigates the problem of event-triggered model-free adaptive iterative learning control (MFAILC) for a class of nonlinear systems over fading channels. The fading phenomenon existing in output channels is modeled as an independent Gaussian distribution with mathematical expectation and variance. An event-triggered condition along both iteration domain and time domain is constructed in order to save the communication resources in the iteration. The considered nonlinear system is converted into an equivalent linearization model and then the event-triggered MFAILC independent of the system model is constructed with the faded outputs. Rigorous analysis and convergence proof are developed to verify the ultimately boundedness of the tracking error by using the Lyapunov function. Finally, the effectiveness of the presented algorithm is demonstrated with a numerical example and a velocity tracking control example of wheeled mobile robots (WMRs).

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) method to approximate them. This instability arises in the presence of eigenvalues that are close to each other. This makes integrating eigendecomposition into deep networks difficult and often results in poor convergence, particularly when dealing with large matrices. While this can be mitigated by partitioning the data into small arbitrary groups, doing so has no theoretical basis and makes it impossible to exploit the full power of eigendecomposition. In previous work, we mitigated this using SVD during the forward pass and PI to compute the gradients during the backward pass. However, the iterative deflation procedure required to compute multiple eigenvectors using PI tends to accumulate errors and yield inaccurate gradients. Here, we show that the Taylor expansion of the SVD gradient is theoretically equivalent to the gradient obtained using PI without relying in practice on an iterative process and thus yields more accurate gradients. We demonstrate the benefits of this increased accuracy for image classification and style transfer., Comment: IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) PREPRINT 2021

With the increasing demand for intelligent transportation systems, short-term traffic flow prediction has become an important research direction. The memory unit of a Long Short-Term Memory (LSTM) neural network can store data characteristics over a certain period of time, hence the suitability of this network for time series processing. This paper uses an improved Gate Recurrent Unit (GRU) neural network to study the time series of traffic parameter flows. The LSTM short-term traffic flow prediction based on the flow series is first investigated, and then the GRU model is introduced. The GRU can be regarded as a simplified LSTM. After extracting the spatial and temporal characteristics of the flow matrix, an improved GRU with a bidirectional positive and negative feedback called the Bi-GRU prediction model is used to complete the short-term traffic flow prediction and study its characteristics. The Rectified Adaptive (RAdam) model is adopted to improve the shortcomings of the common optimizer. The cosine learning rate attenuation is also used for the model to avoid converging to the local optimal solution and for the appropriate convergence speed to be controlled. Furthermore, the scientific and reliable model learning rate is set together with the adaptive learning rate in RAdam. In this manner, the accuracy of network prediction can be further improved. Finally, an experiment of the Bi-GRU model is conducted. The comprehensive Bi-GRU prediction results demonstrate the effectiveness of the proposed method.

The issue of bipartite time-varying formation (BTVF) tracking for linear multiagent systems (MASs) with a leader of unknown input on signed digraphs is investigated. An adaptive nonsmooth protocol is taken in this article that utilizes only the local output feedback information among neighbors and, thus, can avoid employing the eigenvalue information of the Laplacian matrix of the graph. It is proven that if the interaction network of agents containing a spanning tree is structurally balanced, the BTVF tracking can be achieved with a leader of the bounded input via the proposed scheme. This leader-following BTVF includes two time-varying subformations, whose relationship is antagonistic. A convergence analysis of the proposed protocol for MASs is reflected by the Lyapunov method. Finally, the validly numerical simulations are illustrated to show the performance of the proposed schemes.

Unmanned aerial vehicles (UAVs) can be leveraged in mobile crowdsensing (MCS) to conduct sensing tasks at remote or rural areas through computation offloading and data sensing. Nonetheless, both computation offloading and data sensing have been separately investigated in most existing studies. In this paper, we propose a novel cooperative data sensing and computation offloading scheme for the UAV-assisted MCS system with an aim to maximize the overall system utility. First, a multi-objective function is formulated to evaluate the system utility by jointly considering flight direction, flight distance,task offloading proportion, and server offload selection for each UAV. Then, the problem is modeled as a partially observable Markov decision process and a multi-agent actor-critic algorithm framework is proposed to train the strategy network for UAVs. Due to high delay and energy cost caused by communications among multiple agents, we leverage the critic network to model other agents and to seek equilibrium among all UAVs rather than adopting the explicit channel for information exchange. Furthermore, we introduce attention mechanism to enhance the convergence performance in model training phases. Finally, experimental results demonstrate the effectiveness and applicability of our scheme. Compared with baselines, our algorithm shows significant advantages in convergence performance and system utility.

A correlation between fuzzy logic systems (FLS) and zeroing neural networks (ZNN) design is investigated. It is shown that the gain parameter included in ZNN design can be dynamically adjusted over time by means of an appropriate value derived as the output of a properly defined FLS which includes appropriately defined membership functions and fuzzy logic rules. Dynamical systems which are applicable to time-varying rank-deficient matrices are proposed. Convergence properties are investigated and illustrative simulation experiments are performed. Presented simulation experiments confirm the superiority of the FLS proposed in the paper with respect to previously proposed FLS for dynamic adjustment of gain parameters. Furthermore, the superiority of the FLS-based ZNN model over the corresponding ZNN models based on the classical approach in defining the varying-gain parameter is demonstrated.

Complex dynamical systems rely on the correct deployment and operation of numerous components, with state-of-the-art methods relying on learning-enabled components in various stages of modeling, sensing, and control at both offline and online levels. This article addresses the runtime safety monitoring problem of dynamical systems embedded with neural-network components. A runtime safety state estimator in the form of an interval observer is developed to construct the lower bound and upper bound of system state trajectories in runtime. The developed runtime safety state estimator consists of two auxiliary neural networks derived from the neural network embedded in dynamical systems, and observer gains to ensure the positivity, namely, the ability of the estimator to bound the system state in runtime, and the convergence of the corresponding error dynamics. The design procedure is formulated in terms of a family of linear programming feasibility problems. The developed method is illustrated by a numerical example and is validated with evaluations on an adaptive cruise control system.

We consider a population composed of a continuum of agents that seek to maximize a payoff function by moving on a network. The nodes in the network may represent physical locations or abstract choices. The population is stratified, i.e., agents opting for the same choice may not get the same payoff. In particular, we assume payoff functions with diminishing returns, i.e., agents in newer strata of a node receive a smaller payoff compared to older strata. In this first part of two-part work, we model the population dynamics under three choice revision policies, having varying levels of coordination i. no coordination and the agents are selfish, ii. coordination among agents in each node and iii. coordination across the entire population. For the case with selfish agents, we generalize the Smith dynamics to our setting, where we have a stratified population and network constraints. To model nodal coordination, we allow the fraction of population in a node, as a whole, to take the best response to the state of the population in the nodes neighborhood. For the case of population-wide coordination, we explore a dynamics where the population evolves according to centralized gra

This paper presents a novel hierarchical cooperative control strategy to solve the problems of unbalanced State of Charge (SoC), unreasonable load current sharing, and unstable bus voltage for battery storage system (BSS) in islanded DC microgrid. In the communication layer, a neighbor-to-neighbor communication network architecture is constructed in which each battery storage unit (BSU) only communicates information with neighboring nodes, and a multi-agent consensus algorithm is used to iteratively estimate the relevant average global variables. In the main control layer, the droop coefficient is dynamically adjusted by constructing a fast SoC convergence function to ensure that the load current is reasonably distributed based on the rated capacity of each BSU. In the secondary control layer, a virtual voltage drop equalization controller and an average bus voltage compensation controller are designed to eliminate the impact of line impedance mismatch and compensate the average bus voltage. Furthermore, an optimized factor is designed to accelerate the later stage of SoC convergence. Finally, a DC microgrid experimental platform based on StarSim HIL is built, and the results demonstrate that the proposed strategy can achieve the control objectives of fast SoC balance, proportional load current sharing, and bus voltage stability.

The design of fuzzy neural network (FNN) has long been a challenging problem since most methods rely on approximation error to train FNN, which may easily occur overfitting phenomenon to degrade the generalization performance. To improve the generalization performance, a fuzzy neural network with multi-objective optimization algorithm (MOO-FNN) is proposed in this paper. First, the multi-level learning objectives are designed around the generalization performance to guide the training process of FNN. Then, the method utilizes the approximation error, the structure complexity, and the output smoothness indicators instead of a single indicator to improve the evaluation accuracy of generalization performance. Second, a MOO algorithm with continuous-discrete variables is developed to optimize FNN. Then, MOO is able to use a novel particle update method to adjust both the structure and parameters rather than adjust them separately, thereby achieving suitable generalization performance of FNN. Third, the convergence of MOO-FNN is analyzed in detail to guarantee its successful applications. Finally, the experimental studies of MOO-FNN have been performed on model identification of nonlinear systems to verify the effectiveness. The results illustrate that MOO-FNN has a significant improvement over some state-of-the-art algorithms.

This article studies the distributed average tracking (DAT) problem pertaining to a discrete-time linear time-invariant multiagent network, which is subject to, concurrently, input delays, random packet drops, and reference noise. The problem amounts to an integrated design of delay and a packet-drop-tolerant algorithm and determining the ultimate upper bound of the tracking error between agents' states and the average of the reference signals. The investigation is driven by the goal of devising a practically more attainable average tracking algorithm, thereby extending the existing work in the literature, which largely ignored the aforementioned uncertainties. For this purpose, a blend of techniques from Kalman filtering, multistage consensus filtering, and predictive control is employed, which gives rise to a simple yet comepelling DAT algorithm that is robust to the initialization error and allows the tradeoff between communication/computation cost and stationary-state tracking error. Due to the inherent coupling among different control components, convergence analysis is significantly challenging. Nevertheless, it is revealed that the allowable values of the algorithm parameters rely upon the maximal degree of an expected network, while the convergence speed depends upon the second smallest eigenvalue of the same network's topology. The effectiveness of the theoretical results is verified by a numerical example.

As one of the most commonly used clustering methods, the Fuzzy C-means (FCM) clustering strategy extends the notion of hard clustering to associate each pattern with every cluster using a membership function. Although a lot of efforts have been made by the clustering community, it is still unclear how to evaluate the fuzziness of different versions of FCM. To fill this theoretical blank, by observing a family of objective functions, a definition of fuzzy degree is provided to quantify the fuzziness of different versions of FCM according to their dedicated objective functions. Then a general Fuzzy C-Means (GFCM) clustering algorithm is proposed to solve the clustering problem of using FCM under different distance metrics and fuzzy degrees. From the perspective of fuzzy attribute, the using of this fuzzy degree can be used to reveal the essential difference among a group of FCM-based clustering algorithms, and the proposed GFCM achieves the aim of using objective functions to control the fuzziness of clustering results. Additionally, some properties and relations of these FCM-based clustering algorithms under different fuzzy degrees are discussed and the convergence and stability of the proposed GFCM are proved. Finally, extensive experiments have been performed to demonstrate that by comparison with the effect caused by distance metric, the choices of fuzzy degree have a more significant effect and improvement on the performances of a FCM-based clustering algorithm.

This article focuses on the L2-L/H optimization control issue for a family of nonlinear plants by Takagi-Sugeno (T-S) fuzzy approach with actuator failure. First, considering unmeasurable system states, sufficient criteria for devising fuzzy imperfect premise matching dynamic output feedback controller to maintain asymptotic stability while guaranteeing a mixed performance for T-S fuzzy systems are provided. Therewith, in the light of feasible areas of dynamic output feedback controller membership functions (MFs), a new MFs online learning policy using gradient descent algorithm is proposed to learn the real-time values of MFs so as to acquire a better L2-L/H control effect. Different from the traditional method using imperfect premise matching scheme, under the proposed optimization algorithm, the trajectory of mixed performance index is lowered effectively. Afterward, a sufficient criterion is presented for assuring the convergence of the error of cost function. Lastly, the superiority of this online optimization learning policy is confirmed via simulations.

In this article, we investigate the adaptive output tracking control for multiinput-multioutput piecewise affine systems with prescribed performance. Both direct and indirect adaptation approaches are studied. Given a desired trajectory, both control approaches ensure the output tracking error to be confined within a performance bound, which prescribes the steady-state tracking error as well as the transient behavior, such as decaying rate and overshoot. We establish novel common Lyapunov functions without solving the conventional Lyapunov equations. Based on these common Lyapunov functions, the stability of the closed-loop system under arbitrary switching is established. Furthermore, the parameter convergence for both direct and indirect approaches is proved under the persistently exciting condition of the input signals. The dynamic gain adjustment technique is incorporated to counter the singularity problem in the indirect adaptation case. Finally, the numerical simulation validates the effectiveness and correctness of the proposed approaches in both direct and indirect adaptation cases.

This article studies the path planning for an unmanned aerial vehicle (UAV) standoff tracking a narrow-area target in complex environment. Since the target state estimation considerably influences the target tracking performance, the constrained interacting multiple model, which uses the geographic information of narrow-areas to enhance the estimation accuracy, is proposed. Then, based on the obtained estimation results, the dynamic Lyapunov guidance vector field (DLGVF) is proposed, which can guide UAVs to converge to not only the expected standoff distance in the horizontal plane but also the desired height in the vertical plane. Moreover, the DLGVF renders the UAV trajectories flexible and shortens the convergence time by skillfully introducing adjustment parameters. Finally, to simultaneously complete the missions of target tracking and obstacle avoidance, an integrated method based on the DLGVF and the interfered fluid dynamical system is presented. Simulations are implemented to demonstrate that the proposed framework is effective.

It is important to accurately obtain the motion information of the ego vehicle and surrounding vehicles for autonomous vehicles to plan safe trajectories in complicated traffic environments. In this paper, a LiDAR-based estimation method is developed to simultaneously identify the pose and the velocity information of an ego vehicle and its surrounding moving obstacles. Specifically, a pose estimation network is designed to estimate the poses of both the ego vehicle and the obstacles only with the continuous point clouds obtained by the LiDAR mounted on the ego vehicle. In the network, PointNet++ is utilized as the backbone to extract point-wise features and divide the points into the static part and the moving part. The former is used to estimate the ego vehicle's pose, while the latter is applied for the obstacle pose identification. Then, a reduced-order observer is designed to estimate the velocities, whose convergence is proved with the Lyapunov theory. Finally, both simulation and experiment results are provided to show the effectiveness of the proposed method.

In this article, an online RNN-based finite-time formation tracking control (ORNN-FTFTC) is designed to quickly accomplish an assigned formation of nonlinear generalized and heterogeneous multiagent systems with input fault and saturation. Each agent, including the leader and the followers, can possess different relative degrees and control input numbers but the same output for easy task planning. At least one agent must communicate with the leader and the information of neighborhood agents is required to accomplish the assigned formation task. To fulfill the task under the uncertain environment, the proposed ORNN-FTFTC possesses nonlinear filtering formation error with dynamic fractional exponent, nonlinear filtering gain, and the RNN learning compensation of the aggregately uncertain dynamics in each agent. Not only does the nonlinear filtering gain increase as the nonlinear filtering formation error is in the vicinity of zero to achieve its finite-time convergence, but also the new e-modification learning can cover all the value of formation error such that learning weights are stabilized even in an uncertain environment. Finally, an application to a 3D pose from take-off to a steady-formation of hexa-copter unmanned aerial vehicles and unmanned helicopters with initial formation error certifies the feasibility and robustness of the proposed control.

A considerable number of surrogate-assisted evolutionary algorithms (SAEAs) have been developed to solve expensive optimization problems (EOPs) with continuous objective functions. However, in the real-world applications, we may face EOPs with discontinuous objective functions, which are also called EOPs with discontinuous responses (EOPDRs). Indeed, EOPDRs pose a great challenge to current SAEAs. In this paper, a surrogate-assisted differential evolution (DE) algorithm with region division is proposed, named ReDSADE. ReDSADE includes three main strategies: the region division strategy, the Kriging-based search, and the radial basis function (RBF)-based local search. In the region division strategy, we define a new distance measure, called the objective-decision distance. Based on this distance, the evaluated solutions are partitioned into several clusters, and several support vector machine (SVM) classifiers are trained to classify them. These SVM classifiers divide the decision space into several subregions, with the aim of making the objective function continuous in them. In the Kriging-based search, a Kriging model is established in each subregion and combined with DE to search for the optimal solution. In the RBF-based local search, DE is coupled with RBF to search around the best solution found so far, thus accelerating the convergence. By combining these three strategies, ReDSADE is able to solve EOPDRs with limited function evaluations. Three set of test problems and a real-world application are utilized to verify the effectiveness of ReDSADE. The results demonstrate that ReDSADE exhibits good convergence accuracy and convergence speed.