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In order to make redundant robot manipulators (RRMs) track the complex time-varying trajectory, the motion-planning problem of RRMs can be converted into a constrained time-varying quadratic programming (TVQP) problem. By using a new punishment mechanism-combined recurrent neural network (PMRNN) proposed in this article with reference to the varying-gain neural-dynamic design (VG-NDD) formula, the TVQP problem-based motion-planning scheme can be solved and the optimal angles and velocities of joints of RRMs can also be obtained in the working space. Then, the convergence performance of the PMRNN model in solving the TVQP problem is analyzed theoretically in detail. This novel method has been substantiated to have a faster calculation speed and better accuracy than the traditional method. In addition, the PMRNN model has also been successfully applied to an actual RRM to complete an end-effector trajectory tracking task.

Engineering design is traditionally performed by hand: an expert makes design proposals based on past experience, and these proposals are then tested for compliance with certain target specifications. Testing for compliance is performed first by computer simulation using what is called a discipline model. Such a model can be implemented by finite element analysis, multibody systems approach, etc. Designs passing this simulation are then considered for physical prototyping. The overall process may take months and is a significant cost in practice. We have developed a Bayesian optimization (BO) system for partially automating this process by directly optimizing compliance with the target specification with respect to the design parameters. The proposed method is a general framework for computing the generalized inverse of a high-dimensional nonlinear function that does not require, for example,\ gradient information, which is often unavailable from discipline models. We furthermore develop a three-tier convergence criterion based on: 1) convergence to a solution optimally satisfying all specified design criteria; 2) detection that a design satisfying all criteria is infeasible; or 3) convergence to a probably approximately correct (PAC) solution. We demonstrate the proposed approach on benchmark functions and a vehicle chassis design problem motivated by an industry setting using a state-of-the-art commercial discipline model. We show that the proposed approach is general, scalable, and efficient and that the novel convergence criteria can be implemented straightforwardly based on the existing concepts and subroutines in popular BO software packages.

In this article, being different from conventional time-discretization (simply called discretization) formulas, explicit linear left-and-right 5-step (ELLR5S) formulas with sixth-order precision are proposed. The general sixth-order ELLR5S formula with four variable parameters is developed first, and constraints of these four parameters are displayed to guarantee the zero stability, consistence, and convergence of the formula. Then, by choosing specific parameter values within constraints, eight specific sixth-order ELLR5S formulas are developed. The general sixth-order ELLR5S formula is further utilized to generate discrete zeroing neural network (DZNN) models for solving time-varying linear and nonlinear systems. For comparison, three conventional discretization formulas are also utilized. Theoretical analyses are presented to show the performance of ELLR5S formulas and DZNN models. Furthermore, abundant experiments, including three practical applications, that is, angle-of-arrival (AoA) localization and two redundant manipulators (PUMA560 manipulator and Kinova manipulator) control, are conducted. The synthesized results substantiate the efficacy and superiority of sixth-order ELLR5S formulas as well as the corresponding DZNN models.

Iterative learning control (ILC) relies on a finite-time interval output predictor to determine the output trajectory in each trial. Robust ILCs intend to model the uncertainties in the predictor and to guarantee the convergence of the learning process subject to such model errors. Despite the vast literature in ILCs, parameterizing the uncertainties with the stochastic errors in the predictor parameters identified from system I/O data and thus robustifying the ILC have not yet been targeted. This work is devoted to solving such problems in a data-driven fashion. The main contributions are two-fold. First, a data-driven ILC method is developed for LTI systems. The relationship is established between the errors in the predictor matrix and the stochastic disturbances to the system. Its robust monotonic convergence (RMC) is then linked with the closed-loop learning gain matrix that contains the predictor uncertainties and is analyzed based on a closed-form expectation of this gain matrix multiplied with its own transpose, that is, in a mean-square sense (MS-RMC). Second, the data-driven ILC and MS-RMC analysis are extended to nonlinear Hammerstein-Wiener (H-W) systems. The advantages of the proposed methods are finally verified via extensive simulations in terms of their convergence and uncorrelated tracking performance with the stochastic parametric uncertainties.

Model-free control approaches require advanced exploration-exploitation policies to achieve practical tasks such as learning to bipedal robot walk in unstructured environments. In this article, we first construct a comprehensive exploration-exploitation policy that carries quality knowledge about the long-term predictor and the control policy, and the control signal of the model-free algorithms. Therefore, the developed model-free algorithm continues exploration by adjusting its unknown parameters until the desired learning and control are accomplished. Second, we provide an utterly model-free adaptive law enriched with the exploration-exploitation policy and derived step-by-step using the exact analogy of the model-based solution. The obtained adaptive control law considers the control signal saturation and the control signal (input) delay. Performed Lyapunov stability analysis ensures the convergence of the adaptive law that can also be used for intelligent control approaches. Third, we implement the adaptive algorithm in real time on a challenging benchmark system: a fourth-order, coupled dynamics, input saturated, and time-delayed underactuated manipulator. The results show that the proposed adaptive algorithm explores larger state-action spaces and treats the vanishing gradient problem in both learning and control. Also, we notice from the results that the learning and control properties of the adaptive algorithm are optimized as required.

It is known that many-objective optimization problems (MaOPs) often face the difficulty of maintaining good diversity and convergence in the search process due to the high-dimensional objective space. To address this issue, this article proposes a novel multiobjective framework for many-objective optimization (Mo4Ma), which transforms the many-objective space into multiobjective space. First, the many objectives are transformed into two indicative objectives of convergence and diversity. Second, a clustering-based sequential selection strategy is put forward in the transformed multiobjective space to guide the evolutionary search process. Specifically, the selection is circularly performed on the clustered subpopulations to maintain population diversity. In each round of selection, solutions with good performance in the transformed multiobjective space will be chosen to improve the overall convergence. The Mo4Ma is a generic framework that any type of evolutionary computation algorithm can incorporate compatibly. In this article, the differential evolution (DE) is adopted as the optimizer in the Mo4Ma framework, thus resulting in an Mo4Ma-DE algorithm. Experimental results show that the Mo4Ma-DE algorithm can obtain well-converged and widely distributed Pareto solutions along with the many-objective Pareto sets of the original MaOPs. Compared with seven state-of-the-art MaOP algorithms, the proposed Mo4Ma-DE algorithm shows strong competitiveness and general better performance.

We study an optimal targeting problem for super-modular games with binary actions and finitely many players. The considered problem consists in the selection of a subset of players of minimum size such that, when the actions of these players are forced to a controlled value while the others are left to repeatedly play a best response action, the system will converge to the greatest Nash equilibrium of the game. Our main contributions consist in showing that the problem is NP-complete and in proposing an efficient iterative algorithm with provable convergence properties for its solution. We discuss in detail the special case of network coordination games and its relation with the notion of cohesiveness. Finally, we show with simulations the strength of our approach with respect to naive heuristics based on classical network centrality measures.

This article addresses decentralized robust portfolio optimization based on multiagent systems. Decentralized robust portfolio optimization is first formulated as two distributed minimax optimization problems in a Markowitz return-risk framework. Cooperative-competitive multiagent systems are developed and applied for solving the formulated problems. The multiagent systems are shown to be able to reach consensuses in the expected stock prices and convergence in investment allocations through both intergroup and intragroup interactions. Experimental results of the multiagent systems with stock data from four major markets are elaborated to substantiate the efficacy of multiagent systems for decentralized robust portfolio optimization.

This article proposes a novel fixed-time converging forward-backward-forward neurodynamic network (FXFNN) to deal with mixed variational inequalities (MVIs). A distinctive feature of the FXFNN is its fast and fixed-time convergence, in contrast to conventional forward-backward-forward neurodynamic network and projected neurodynamic network. It is shown that the solution of the proposed FXFNN exists uniquely and converges to the unique solution of the corresponding MVIs in fixed time under some mild conditions. It is also shown that the fixed-time convergence result obtained for the FXFNN is independent of initial conditions, unlike most of the existing asymptotical and exponential convergence results. Furthermore, the proposed FXFNN is applied in solving sparse recovery problems, variational inequalities, nonlinear complementarity problems, and min-max problems. Finally, numerical and experimental examples are presented to validate the effectiveness of the proposed neurodynamic network.

The general tensor-based methods can recover missing values of multidimensional images by exploiting the low-rankness on the pixel level. However, especially when considerable pixels of an image are missing, the low-rankness is not reliable on the pixel level, resulting in some details losing in their results, which hinders the performance of subsequent image applications (e.g., image recognition and segmentation). In this article, we suggest a novel multiscale feature (MSF) tensorization by exploiting the MSFs of multidimensional images, which not only helps to recover the missing values on a higher level, that is, the feature level but also benefits subsequent image applications. By exploiting the low-rankness of the resulting MSF tensor constructed by the new tensorization, we propose the convex and nonconvex MSF tensor train rank minimization (MSF-TT) to conjointly recover the MSF tensor and the corresponding original tensor in a unified framework. We develop the alternating directional method of multipliers (ADMMs) to solve the convex MSF-TT and the proximal alternating minimization (PAM) to solve the nonconvex MSF-TT. Moreover, we establish the theoretical guarantee of convergence for the PAM algorithm. Numerical examples of real-world multidimensional images show that the proposed MSF-TT outperforms other compared approaches in image recovery and the recovered MSF tensor can benefit the subsequent image recognition.

Regression in a sparse Bayesian learning (SBL) framework is usually formulated as a global optimization problem with a nonconvex objective function and solved in a majorization-minimization framework where the solution quality and consistency depend heavily on the initial values of the used algorithm. In view of the shortcomings, this article presents an SBL algorithm based on collaborative neurodynamic optimization (CNO) for searching global optimal solutions to the global optimization problem. The CNO system consists of a population of recurrent neural networks (RNNs) where each RNN is convergent to a local optimum to the global optimization problem. Reinitialized repetitively via particle swarm optimization with exchanged local optima information, the RNNs iteratively improve their searching performance until reaching global convergence. The proposed CNO-based SBL algorithm is almost surely convergent to a global optimal solution to the formulated global optimization problem. Two applications with experimental results on sparse signal reconstruction and partial differential equation identification are elaborated to substantiate the superiority and efficacy of the proposed method in terms of solution optimality and consistency.

As the controller parameter adjustment process is simplified significantly by using learning algorithms, the studies about learning-based control attract a lot of interest in recent years. This article focuses on the intelligent servo control problem using learning from desired demonstrations. Compared with the previous studies about the learning-based servo control, a control policy using the broad learning system (BLS) is developed and first applied to a microrobotic system, since the advantages of the BLS, such as simple structure and no-requirement for retraining when new demos' data is provided. Then, the Lyapunov theory is skillfully combined with the complex learning algorithm to derive the controller parameters' constraints. Thus, the final control policy not only can obtain the movement skills of the desired demonstrations but also have the strong ability of generalization and error convergence. Finally, simulation and experimental examples verify the effectiveness of the proposed strategy using MATLAB and a microswimmer trajectory tracking system.

This paper deals with nonconvex stochastic optimization problems in deep learning and provides appropriate learning rates with which adaptive learning rate optimization algorithms, such as Adam and AMSGrad, can approximate a stationary point of the problem. In particular, constant and diminishing learning rates are provided to approximate a stationary point of the problem. Our results also guarantee that the adaptive learning rate optimization algorithms can approximate global minimizers of convex stochastic optimization problems. The adaptive learning rate optimization algorithms are examined in numerical experiments on text and image classification. The experiments show that the algorithms with constant learning rates perform better than ones with diminishing learning rates.

Checking uniform attractivity of a time-varying dynamic system without a strict Lyapunov function is challenging as it requires the characterization of the limiting behavior of a set of trajectories. In the context of hybrid nonlinear time-varying (NLTV) systems, characterizing such limiting or convergent behaviors is even harder due to the complexity stemming from both continuous-time variations as well as discrete-time jumps. In this work, an extension of the standard hybrid time domain is introduced to define limiting behaviors, using set convergence, when time approaches either positive infinity or negative infinity. In particular, it is shown how to characterize limiting behaviors under the condition that an output signal approaches zero. Such limiting behaviors and their associated limiting systems can be used to verify uniform global attractivity. Particularly, a generalization of the classic Krasovskii-LaSalle theorem is obtained for hybrid time-varying systems. Two examples are used to demonstrate the effectiveness of the results.

A multivariable finite-time control algorithm is proposed for double integrator systems with matched disturbances. The remarkable feature of the developed method is to ensure the finite-time stability of the closed-loop system with uniformly bounded control signal with respect to arbitrary initial conditions. The convergence criteria is derived by using the Lyapunov-based techniques, and the upper bound of the control signal can be calculated based on the obtained criteria. Finally, the effectiveness of the proposed algorithm is confirmed by some numerical simulations.

We propose decentralized primal-dual methods for cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific convex functions over conic constraint sets defined by agent-specific nonlinear functions; hence, the optimal consensus decision should lie in the intersection of these private sets. Under the strong convexity assumption, we provide convergence rates for sub-optimality, infeasibility, and consensus violation in terms of the number of communications required; examine the effect of underlying network topology on the convergence rates., A preliminary result of this paper was presented in arXiv:1706.07907 by Hamedani and Aybat. In this paper, we generalize our results to the setting where agent-specific constraints are defined by nonlinear functions rather than linear ones which greatly improves the modeling capability. This generalization requires a more complicated analysis which is studied in this separate arXiv submission

This work proposes a novel event-triggered exponential supertwisting algorithm (ESTA) for path tracking of a mobile robot. The proposed work is divided into three parts. In the first part, a fractional-order sliding surface-based exponential supertwisting event-triggered controller has been proposed. Fractional-order sliding surface improves the transient response, and the exponential supertwisting reaching law reduces the reaching phase time and eliminates the chattering. The event-triggering condition is derived using the Lipschitz method for minimum actuator utilization, and the interexecution time between two events is derived. In the second part, a fault estimator is designed to estimate the actuator fault using the Lyapunov stability theory. Furthermore, it is shown that in the presence of matched and unmatched uncertainty, event-trigger-based controller performance degrades. Hence, in the third part, an integral sliding-mode controller (ISMC) has been clubbed with the event-trigger ESTA for filtering of the uncertainties. It is also shown that when fault estimator-based ESTA is clubbed with ISMC, then the robustness of the controller increases, and the tracking performance improves. This novel technique is robust toward uncertainty and fault, offers finite-time convergence, reduces chattering, and offers minimum resource utilization. Simulations and experimental studies are carried out to validate the advantages of the proposed controller over the existing methods.

This article is concerned with the intermittent estimator-based mixed passive and H∞ control for the high-speed train (HST) with multiple noises, actuator stochastic fault, and sensor packet loss. First, an intermittent estimator is designed to track the undetectable status of HSTs in response to only partial information available due to sensor failures. Then, two different stability criteria are developed by adopting two different Lyapunov function strategies. Simultaneously, in order to reduce the control cost and accelerate the convergence time, two different algorithms are designed. It is worth emphasizing that different from the existing results of HST subject to actuator fault, this article adopts a more flexible fault representation mode, namely, semi-Markov switching mode, which is more in line with the practical background and has a higher valuable application. Especially, the Lyapunov function designed in this article can drive the system state to decrease monotonically in both the ``working interval'' and the ``rest interval,'' so as to avoid the phenomenon of state impulsive jump. Finally, through the test of HST experimental value of Japan's Shinkansen, the simulation results show the effectiveness and rationality of the proposed control method and also make a comparative analysis with related works, to prove the advantages of the control technology proposed in this article.

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.

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.

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.

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.

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.

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).

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

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.