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Online transfer learning (OTL) has attracted much attention in recent years. It is designed to handle the transfer learning tasks, where the data of the target domain isn’t available in advance but may arrive in an online manner, which may be a more realistic scenario in practice. However, there typically are two limitations of existing OTL algorithms. 1) Existing OTL algorithms are based on shallow online learning models (SOLMs), e.g., linear or kernel models. Due to this limitation of SOLMs they cannot effectively learn complex nonlinear functions in complicated application and the OTL algorithms based on SOLMs cannot either. 2) Existing algorithms only utilize the latest arrived instance to adjust the model. In this way, the previously arrived instances are not utilized. It may be better to utilize the previously arrived instances as well. In this paper, to overcome the abovementioned two limitations, a buffered online transfer learning (BOTL) algorithm is proposed. In the proposed BOTL algorithm, the learner is designed as a deep learning model, referred to as Online Hedge Neural Network (OHNN). In order to enable the OHNN to be effectively learned in an online manner, we propose a buffered online learning framework that utilizes several previously arrived instances to assist learning. Further, to enhance the performance of the OHNN, a model learned in the source domain is transferred to the target domain. The regret bound of the proposed BOTL algorithm is analyzed theoretically. Experimental results on realistic datasets illustrate that the proposed BOTL algorithm can achieve lower mistake rate than the algorithms compared.

Based on practical applications of the complex-valued Sylvester equation and the effectiveness of zeroing neural network (ZNN) in solving time-varying problems, two discrete nonlinear and noise-tolerant ZNN (DNN-TZNN) models are proposed to solve the time-varying augmented complex Sylvester (TACS) equation by using the Adams-Bashforth formula to discretize the continuous nonlinear and noise-tolerant ZNN (CNN-TZNN) model. The presented DNN-TZNN models are divided into two types: DNN-TZNK and DNN-TZNU models, according to whether the derivative information is known or not in the CNN-TZNN design formula. Compared with the continuous ZNN methods, the proposed DNN-TZNN models are more innovative, and compared with other discrete ZNN methods, the convergence speed of the DNN-TZNN models is much faster and more accurate. Through the theoretical analysis, the superior convergence and strong robustness of the DNN-TZNN models are guaranteed. At last, the simulative experiments not only verify the correctness of the theoretical analysis but also demonstrate the availability of the DNN-TZNN models in solving the TACS problem.

Reinforcement learning (RL) has enjoyed considerable success in application to nonlinear systems. However, very few RL-based works that explicitly address the control problem of MIMO nonlinear systems with subject to actuator failures. In this work, we develop a fault-tolerant adaptive tracking control method fused with an echo state network (ESN) driven by reinforcement learning for Euler-Lagrange systems subject to actuation faults. The proposed control includes an associative search network (ASN), a control gain network (CGN), and an adaptive critic network (ACN), with ASN to estimate the unknown items of the control system, CGN to deal with the time-varying and unknown control gains matrix, and ACN to generate the reinforcement signal, all together ensuring stable tracking and accommodate modeling uncertainties and actuation failures. Different from traditional reinforcement learning controllers that utilizes radial basis function neural networks (RBFNN) or fuzzy systems, the proposed one adopts an echo state network, a paradigm of recurrent neural networks, to implement the ASN, ACN and CGN, resulting in enhanced learning capabilities and stronger robustness against external uncertainties and disturbances, thus better control performance.

This paper proposes a novel reinforcement learning-based attitude tracking control strategy for combined spacecraft takeover maneuvers with completely unknown dynamics. One major issue in the context of combined spacecraft attitude takeover control is that the accurate dynamic model is highly nonlinear, complex and costly to identify online, which makes it impractical for control design. To address this issue, we take the advantage of the Q-learning algorithm to acquire the control strategy directly from system input/output measurement data in a model-free manner, and thus the online inertia parameter identification procedure is avoided. More specifically, first, the attitude tracking is formulated as a regulation problem by introducing an argumented system, where the system dynamic model is still required in control design. Then, in order to achieve a model-free control strategy, an online policy-iteration (PI) Q-learning procedure is derived to solve the Bellman optimality equation by utilizing the generated measurement data. In theoretical analysis, it is proved that the iteration sequences of Q value function and control strategy can converge to the optimal ones. In addition, rigorous proof of the stability and monotonicity guarantees of the proposed control strategy are also provided. Furthermore, for the purpose of online implementation, off-policy learning scheme is employed to find the optimal Q value function approximator with neural network structure after data-collection phase. Numerical simulations are exhibited to validate the effectiveness of the proposed strategy.

Many industrial applications result in the constrained underdetermined nonlinear system (UNS) that needs to be solved. The existing solutions are reported to the constrained UNS with time-invariant coefficients, and they may not perform well for the time-variant case. In this paper, we attempt to address the above limitation by providing a new discrete-time zeroing neural network (DTZNN) for solving the time-variant UNS (TVUNS) under bound constraint. Specifically, the bound-constrained TVUNS (BC-TVUNS) is first transformed into a mixed nonlinear system by introducing a nonnegative variable. Then, a continuous-time ZNN (CTZNN) model is established to solve such a mixed system as well as the BC-TVUNS. By employing a special difference formula to discretize the CTZNN model, the new DTZNN model is thus proposed to obtain the solution of the BC-TVUNS. Theoretical analysis and comparative numerical results are presented to validate the effectiveness of the proposed DTZNN model over the previous DTZNN models. The DTZNN application potential is further indicated on the basis of the simulations on a dual-arm redundant robot using the proposed model.

In this paper, the decentralized learning scheme for nonlinear systems with mismatched interconnections is developed by using the off-policy integral reinforcement leaning algorithm. First, the decentralized control of the overall system is transformed into the optimal control of each subsystem by introducing an auxiliary control. In order to relax the knowledge of system dynamics, a model-free policy iteration algorithm is derived based on the off-policy integral reinforcement learning. Then, the model-free policy iteration algorithm is used to solve the related Hamilton-Jacobi-Bellman equations, where only the collected system data is required. For implementation purpose, neural networks are employed to approximate the optimal cost functions and the optimal control policies, respectively. Moreover, the least squares method and the experience replay technique are combined to learn neural network weights. Finally, a mismatched interconnected system and a photovoltaic power system are presented to verify the effectiveness of the proposed algorithm.

Noise and physical constraints of redundant manipulators are the two major challenges in the repetitive motion planning (RMP) problems. Therefore, this paper proposed a power-exponent-type modified recurrent neural network (PET-MRNN) to simultaneously address both noise and physical constraints. Moreover, PET-MRNN model is activated by a new Sbp-sinh type nonlinear activation function proposed in this paper. The Sbp-sinh type activation function is first applied to such time varying quadratic program (TVQP) solving and possesses excellent convergence performance. Theoretical analysis proves that the PET-MRNN model can completely eliminate noise disturbance through learning and compensation during the convergence process, and then converge the residual error to zero and obtain the theoretical solution. Finally, simulation and experiments further proved the superiority of the PET-MRNN and the Sbp-sinh type activation function.

An event-triggered tracking control problem is investigated for a class of unknown nonlinear systems in this paper. First, to approximate the unknown function, the radial basis function neural network is used. Then, we propose an event-triggered adaptive neural network control scheme with dynamic gain. Both the event-triggered mechanism in the controller-to-actuator channel and the dynamic gain in the sensor-to-controller channel are considered to reduce the communication load between the controller and the actuator and in the meantime to alleviate the burden of parameter adjustment as well. This scheme makes full use of the advantage that the dynamic gain is driven by the tracking error to ensure that the system output signal can track the reference signal within a prespecified accuracy without adjusting the parameters in use. Moreover, a detailed theoretical proof is given to illustrate that Zeno behavior can be excluded under the designed event-triggered controller. Finally, a simulation example is provided to show the effectiveness of our control scheme.

This paper presents a dynamic neural network based adaptive impedance control method for redundant robots under multiple physical constraints. In order to provide optimal contact performance without an accurate environment model, an adaptive impedance learning method is proposed to establish the optimal interaction between robot and environment. In the inner loop, a theoretical framework of constraint optimization is constructed, and then a dynamic neural network is established to compensate the nonlinear dynamics, and compliance to physical limitations is also satisfied. These limitations include joint angle restriction, angular velocity restriction, angular acceleration restriction, and torque restriction. Theoretical analysis proves the stability of the closed loop system. Numerical results show the effectiveness of the proposed control scheme.

This paper develops an event-triggered optimal control method that can deal with asymmetric input constraints for nonlinear discrete-time systems. The implementation is based on an explainable global dual heuristic programming (XGDHP) technique. Different from traditional GDHP, the required derivatives of cost function in the proposed method are computed by explicit analytical calculations, which makes XGDHP more explainable. Besides, the challenge caused by the input constraints is overcome by the combination of a piece-wise utility function and a bounding layer of the actor network. Furthermore, an event-triggered mechanism is introduced to decrease the amount of computation, and the stability analysis is provided with fewer assumptions compared to most existing studies that investigate event-triggered discrete-time control using adaptive dynamic programming. Two simulation studies are carried out to demonstrate the applicability of the constructed approach. The results present that the developed event-triggered XGDHP algorithm can substantially save the computational load, while maintain comparable performance with the time-based approach.

Transient performance of aero-engine determines the maneuverability of aircraft. The optimal control schedule can tap the potential transient performance with subject to each constraint. Thus the transient time can be minimized with the optimal transient control schedule. This transient schedule is described by a strong constrained and nonlinear problem. It is therefore challenging to present an optimal method to achieve the best transient schedule. Motivated by solving this problem, a surrogate-assisted optimization framework is presented by using the learning capability of neural networks. It is achieved by presenting a sequential ensemble radial basis function (RBF) neural network-based optimization (SERO) algorithm. The advantage of the RBF neural network such as excellent prediction accuracy is taken and integrated into the surrogate-assisted optimization algorithm to improve the algorithm performance. With the application of the proposed scheme, the global optimization schedule is guaranteed for aero-engine transient control. Numerical validation is finally carried out by applying the presented optimization framework to a mixed-flow aero-engine transient control schedule. It is demonstrated that the SERO approach can minimize the transient process time despite any constraint at any time.

This paper investigates the attack isolation (AI) and attack location (AL) problems for a cyber-physical system (CPS) based on the combination of the H-infinity observer and the zonotope theory, where the real control plant in the physical layer is a nonlinear complex network system. Firstly, for actuator AI and AL purposes, two robust H-infinity observers are designed and the stabilities of them are analyzed based on linear matrix inequalities (LMIs). Secondly, the zonotope theory is used to the error dynamic system of the H-infinite observer such that it can calculate iteratively the interval state estimation if the CPS has no attacks. Third, two residuals are constructed and their interval estimates are also given, and furthermore, based on the residual interval estimates, both actuator AI and AL schemes are developed. Besides, sensor AI and AL issues are discussed by modifying the actuator AI and AL schemes. Finally, the effectiveness of the proposed methods is illustrated through a simulation example.

Autoencoders are widely used in many scientific disciplines for their good performance as so-called building blocks of deep learning. Furthermore, they have a pronounced capability for dimensionality reduction. In this paper it is shown that autoencoders can additionally be used not only to detect but to qualify dependencies among the parameters of input data sets. For doing so, a two-step approach is proposed. Herein, the identical mapping of the input data to the output layer is done with a stacked autoencoder. Evaluating respective sensitivity measures yields the sought interrelations between the input parameters, if there are any. To verify the new approach, numerical experiments are conducted with synthesized data where linear or nonlinear dependencies between the input parameters are known a priori. It is shown that the two-step approach automatically detects these dependencies for all investigated cases.

Although robust regulation problem has been well studied, solving robust tracking control via online learning has not been fully solved, in particular for nonlinear systems. This paper develops an online adaptive learning technique to complete the robust tracking control design for nonlinear uncertain systems, which uses the ideas of adaptive dynamic programming (ADP) proposed for optimal control. An augmented system is first constructed using the tracking error and reference trajectory, so as to reformulate the tracking control into a modified robust regulation problem. Then, an equivalence between the robust control and the optimal control is established by using a constructive discounted cost function, which allows to design the robust control by tackling the optimal control of its nominal system. Then, the derived Hamilton-Jacobi-Bellman (HJB) equation is solved by training a critic neural network (NN). Finally, an adaptive learning algorithm is adopted to online directly update the unknown NN weights, where the convergence can be guaranteed. The closed-loop system stability is rigorously proved and extensive simulation results are given to show the effectiveness of the developed learning algorithm.

In this paper, we consider various schemes of sequence resampling in reservoir computing models for nonlinear time series prediction. These schemes can enrich the features used for training the readout part with batch learning and lead to better prediction performance. To implement these schemes, first, we introduce a modular approach for constructing multi-reservoir ESN models by assembling encoding and decoding modules. The encoding module is composed of a resampling unit, a group-wise reservoir unit, and a collection unit, for extracting various features from a sequence. The decoding module is a linear regressor which is trainable to produce desired outputs. Then, we propose three novel multi-reservoir ESN models, DeepESN with Every-layer Sequence Resampling (DeepESN-ESR), DeepESN with Last-layer Sequence Resampling (DeepESN-LSR), and GroupedESN with Input-layer Sequence Resampling (GroupedESN-ISR). These three models provide demonstrations of sequence resampling on multi-reservoir ESN models. Numerical results on five challenging nonlinear time-series prediction tasks show that the proposed models outperform some state-of-the-art multi-reservoir ESN models. An evaluation of computational time shows that our proposed three models require less computational cost for learning than many existing multi-reservoir ESN models in practice. Moreover, a comprehensive comparative analysis reveals that our proposed models are able to memorize longer temporal information and generate richer dynamics from the reservoir states than some existing models. The proposed schemes for extracting various features hidden in a sequence of reservoir states can be widely leveraged in other reservoir computing systems for improving their performance in nonlinear time series prediction.

This paper investigates flocking problems with uncertain nonlinear multi-agent systems. Two distributed adaptive event-triggered control algorithms are proposed for leaderless and leader-follower flocking, separately. According to Lyapunov stability theory, under the proposed control protocols, we obtain some sufficient conditions to ensure stable flocking motion and maintain connectivity of network topology. And it is proven that there is a positive lower limit of the interval between any two trigger events, which indicates that the Zeno behavior will not occur. As a result, communication bandwidth resources are effectively saved on the premise of stable flocking. Lastly, numerical simulations are presented to verify the availability of the theoretical results.

This paper investigates the finite-time stabilization (FTS) problem of leakage delay on complex-valued bidirectional associative memory (BAM) neural networks (CVBAMNNs) with time delays via decomposition approach. This analysis is on the basis of some novel sufficient conditions that the FTS of CVBAMNNs are obtained via Lyapunov functional and upper right Dini derivative concepts. The complex-valued nonlinear function is divided into its real and imaginary components to a set of criteria for the FTS using decomposition technique of CVBAMNNs. We develop feedback controllers in the context of the double-layer structure of the CVBAMNNs. Finally, one numerical example is offered to show the availability of the findings achieved.

Memristive spiking neural networks (MSNNs) have great potential to process information with higher efficiency and lower time latency than conventional artificial neural networks (ANNs). However, MSNNs still lack effective hardware-based training algorithms to achieve comparable performance to the mature ANNs. Therefore, a multilayer locally-connected (LC) MSNN is proposed to realize high performance with self-adaptive and in-situ learning. In the LC-MSNN, spatial and temporal interactions are introduced to activate hidden neurons spontaneously; synaptic weights are updated locally with spike-time-dependent plasticity (STDP) by pulse scheme including processing and updating phases; nonlinear conductance response (CR) is utilized to realize the adjustive learning rate. The LC-MSNN is comprehensively verified and benchmarked with the MNIST dataset. Moreover, self-adaptive activations of the hidden neurons are investigated by extracting and visualizing their internal states and related features; the adjustive learning rate is studied in different nonlinear CR. Effects of non-idealities including finite resolution, device-to-device variation, and yield, are also taken into consideration in the LC-MSNN. Simulation results show the LC-MSNN has better performance (maximum recognition rate of 97.4%) and robustness to non-idealities. Therefore, this method is a hardware-friendly algorithm and can be applied to realize high-performance SNNs in a memristor-based hardware system.

This paper studies the stability and dissipativity issue for neural networks (NNs) with time-varying delay. Firstly, an α 2 -dependent reciprocally convex inequality is presented, which unifies the traditional reciprocally convex inequality and the improved reciprocally convex inequality as its special cases. Secondly, by using the α 2 -dependent reciprocally convex inequality, a tight upper bound on the time-derivative of the Lyapunov-Krasovskii functional (LKF) is obtained, then the analysis and calculation is simplified due to no other nonlinear terms being introduced. As a result, some sufficient conditions are obtained which can be used to ensure the stability and dissipativity of delayed NNs. Finally, simulations are provided to verify the superiority of the presented method.

In this paper, the leader-following consensus of nonlinear multi-agent systems with time delay and aperiodically intermittent communications is investigated. Compared with the intermittent communications for multi-agent systems in previous literature, we relax the periodicity or quasi-periodicity of the intermittent communications and render the intermittent communications to be completely aperiodic. The concepts of average communication ratio and average communication period are adapted to characterize the distributions of communication time and non-communication time. Then the consensus problem for the studied systems with large time delay and small time delay is studied, respectively. Especially, for the case of small time delay, the upper bound of time delay is assumed to be less than the average communication length (average communication ratio × average communication period), but can be larger than some communication lengths, which is less conservative. Finally, numerical examples are provided to show the effectiveness of the main results.

Activation function is an important component of the convolutional neural network. Recently, nonlinear nonmonotonic activation functions such as Swish and Mish have illustrated good performance in deep learning structures. In this paper, we propose a new nonlinear nonmonotonic activation function called Logish, which can be represented by f ( x ) = x · ln [ 1 + sigmoid ( x ) ] . Firstly, we take the logarithmic operation to reduce the numerical range of sigmoid ( x ) + 1 , then we employ variable x to make the negative output have a strong regularization effect. Furthermore, we evaluate the image classification performance of Logish and its variant f ( x ) = α x · ln [ 1 + sigmoid ( β x ) ] in simple and complex networks with top–1 accuracy. Experimental results demonstrate that Logish’s variant ( α = 1 , β = 10 ) can achieve 94.8% top-1 accuracy with ResNet–50 network on CIFAR 10 dataset, and can reach 99.24% top-1 accuracy with DenseNet on MNIST dataset and 88.52% top-1 accuracy with SE-Inception-v4 network on SVHN dataset respectively. It is higher than the Sigmoid, Tanh, ReLU, Swish and Mish activation functions in the corresponding dataset. It also verifies the performance and effectiveness of Logish.

This paper investigates the distributed output tracking problem via linear sampled-data control for a class of uncertain nonlinear multi-agent systems. Specifically, for the case where the graph topology is directed and the leader is the neighbor of only a small portion of followers, by combining the backstepping method with sampled-data method, a series of linear sampled-data controllers are obtained. Stability analysis is performed by using calculus, comparison principle and so on. The main results of this paper are concluded that all the states of the closed-loop system are globally bounded and the output tracking errors can be tuned arbitrarily small. Finally, a numerical example is given to verify the validity of the conclusion.

Using neural networks to address data-driven problems often entails dealing with uncertainties. However, the propagation of uncertainty through a network’s nonlinear layers is usually a bottleneck, since the existing techniques designed to transmit Gaussian distributions via moment estimation are not capable of predicting non-Gaussian distributions. In this study, a Gaussian-mixture-based uncertainty propagation scheme is proposed for neural networks. Given that any input uncertainty can be characterized as a Gaussian mixture with a finite number of components, the developed scheme actively examines each mixture component and adaptively split those whose fidelity in representing uncertainty is deteriorated by the network’s nonlinear activation layers. A Kullback–Leibler criterion that directly measures the nonlinearity-induced non-Gaussianity in post-activation distributions is derived to trigger splitting and a set of high-precision Gaussian splitting libraries is established. Four uncertainty propagation examples on dynamic systems and data-driven applications are demonstrated, in all of which the developed scheme exhibited exemplary fidelity and efficiency in predicting the evolution of non-Gaussian distributions through both recurrent and multi-layer neural networks.

Existing fixed-time adaptive neural controllers for uncertain multi-input/multi-output (MIMO) systems with unknown nonlinear interactions only ensure practical fixed-time stabilization or require extra assumptions on system nonlinear functions. To remove these limitations and improve the result to fixed-time stabilization, a dynamic switched Lyapunov function candidate is newly proposed, based on which a novel direct adaptive neural strategy is developed to design fixed-time stable controllers for MIMO systems. To overcome the difficulty in establishing fixed-time stability in the presence of unknown interactions, a two-step Lyapunov function analysis method is proposed to prove that the tracking errors asymptotically converge to preassigned values within a fixed time. Simulation studies substantiate the methods developed.

We present a novel, accurate, fast, and robust physics-informed neural network method for solving problems involving differential equations (DEs), called Extreme Theory of Functional Connections, or X-TFC. The proposed method is a synergy of two recently developed frameworks for solving problems involving DEs: the Theory of Functional Connections TFC, and the Physics-Informed Neural Networks PINN. Here, the latent solution of the DEs is approximated by a TFC constrained expression that employs a Neural Network (NN) as the free-function. The TFC approximated solution form always analytically satisfies the constraints of the DE, while maintaining a NN with unconstrained parameters. X-TFC uses a single-layer NN trained via the Extreme Learning Machine (ELM) algorithm. This choice is based on the approximating properties of the ELM algorithm that reduces the training of the network to a simple least-squares, because the only trainable parameters are the output weights. The proposed methodology was tested over a wide range of problems including the approximation of solutions to linear and nonlinear ordinary DEs (ODEs), systems of ODEs, and partial DEs (PDEs). The results show that, for most of the problems considered, X-TFC achieves high accuracy with low computational time, even for large scale PDEs, without suffering the curse of dimensionality.

In the paper, data-driven finite-horizon robust formation-containment control scheme is developed based on integral reinforcement learning and zero-sum game for perturbed multi-agent networks with completely unknown nonlinear dynamics. At first, distributed finite-time sliding mode estimators are designed to obtain the desired states of leaders and followers, respectively. Then finite-horizon robust leader formation control and follower containment control are achieved based on proposed model-free integral reinforcement learning algorithms implemented by critic-actor-disturbance structure, in the framework of multi-player zero-sum game where the non-quadratic performance index for each agent considers the influence of saturated inputs and disturbances of local neighbors thoroughly. Furthermore, it is proved that the whole network has bounded L 2 gain robust stability and Nash equilibrium of zero-sum game exists. Simulation results are provided to demonstrate the effectiveness of the proposed scheme.

Deep learning has been growing in popularity for soft sensor modeling of nonlinear industrial processes, infeuality-related variables. However, applications may be highly nonlinear, and the quantity of labeled samples is considerably limited. The extraction of relevant information from abundant unlabeled data is becoming an area of increasing interest in soft-sensor development. A novel ensemble deep relevant learning soft sensor (EDRLSS) modeling framework based on stacked autoencoder (SAE), mutual information (MI), and bagging-based strategy is proposed. SAE is trained layer-by-layer with MI analysis conducted between targeted outputs and learned hidden representations to evaluate and weight the current layer representations. The proposed method eliminates irrelevant information and weights the retained features to highlight the most relevant representations. Thus, the approach extracts deep representative information. Besides, a bagging-based ensemble strategy is applied to improve the soft-sensor performance and reliability. Two real-world industrial nonlinear processes are used to evaluate the EDRLSS framework performance. The results show enhanced prediction performance compared to other state-of-the-art and traditional methods.

In this paper, adaptive neural tracking control problem is considered for non-strict-feedback high-order nonlinear systems with quantized input signal. Compared with the logarithmic quantizer, the quantizer introduced in this paper can avoid chattering problem. The dynamic surface control (DSC) technique is introduced to solve the problem of ‘explosion of complexity’, which is appeared in the classic adaptive backstepping control of high-order nonlinear systems. The structural properties of radial basis function neural networks (RBF NNs) are used to simplify the design difficulty from the functions of whole state variables. According to the classic adaptive backstepping technique and neural network algorithm, an output tracking controller is designed, which can guarantee that all the signals of the closed-loop system are semiglobally uniformly bounded and the output of the system can track the reference signal. Finally, a numerical example is presented to verify the effectiveness of the proposed method.

This paper designs a novel online event-based near-optimal control scheme for multi-player nonzero-sum (NZS) games with partially unknown system dynamics. With the introduction of event-triggered mechanism (ETM), the repetitive computing burdens and communication loads of the signals are largely alleviated. Under the event-triggered mechanism, the framework of identifier-critic is structured to solve the coupled Hamilton–Jacobi equations (CHJEs) for NZS games. A feedforward neural network (FNN) is employed to construct an identifier to learn the unknown dynamics of the nonlinear system. The critic network for each player utilizes a modified tuning law, which is composed of three terms, to seek for the approximated optimal control schemes. Besides the conventional term derived from the gradient descent method, the second term derived from the experience replay (ER) technique utilizes the historical state data to update the critic network weight vector so as to remove the persistence of excitation (PE) condition. In addition, a novel term is added to stabilize the closed-loop systems. Owing to the stabilizing term, there is no need for the initial stabilizing control. In theory, the uniform ultimate boundedness (UUB) properties of the system states and the critic network weight errors are proved by utilizing Lyapunov theorem. Furthermore, the minimal intersample time is proved to be lower bounded with a positive constant which means that the Zeno behavior is excluded during the learning phases. Finally, we show the validity of the designed algorithm via simulating two examples.

Nonlinear and nonconvex optimization problem (NNOP) is a challenging problem in control theory and applications. In this paper, a novel mixture varying-gain dynamic learning network (MVG-DLN) is proposed to solve NNOP with inequality constraints. To do so, first, this NNOP is transformed into some equations through Karush–Kuhn–Tucker (KKT) conditions and projection theorem, and the neuro-dynamics function can be obtained. Second, the time varying convergence parameter is utilized to obtain a faster convergence speed. Third, an integral term is used to strengthen the robustness. Theoretical analysis proves that the proposed MVG-DLN has global convergence and good robustness. Three numerical simulation comparisons between FT-FP-CDNN and MVG-DLN substantiate the faster convergence performance and greater robustness of the MVG-DLN in solving the nonlinear and nonconvex optimization problems.

Hyperspectral unmixing (HU) is regarded as an indispensable preprocessing procedure for many field of spectral data analysis because of the existence of mixed pixels. However, the unmixing algorithms are implemented under the presupposition of special mixing models. In other words, any unmixing algorithm only works on a special mixing model of the spectra. This leads to low generalization performance of most unmixing algorithms. To mitigate this problem, a robust unmixing method is proposed, which exploits dual views with adaptive weights for HU (AwDvHU). The proposed method utilizes multi-kernel learning to construct a high-dimensional space that can reflect the nonlinear interaction between spectra optimally. Then, through fusing the unmixing object of original data and the mapped high-dimensional features, the AwDvHU method takes full advantage of the complementary characteristics of features in dual views. Moreover, the AwDvHU method automatically learns the weights for dual views according to the importance of different feature spaces. Its effectiveness in unmixing is verified by experimental results both on the synthetic and real data.

This paper focuses on the design of online event-triggered optimal control strategy for multi-player zero-sum games (MP-ZSGs) with control constraints when the system model is partially unknown. Non-quadratic functions are utilized to construct the cost functions under the condition of control constraints. The proposed algorithm is designed based on the framework of identifier-critic networks. The unknown drift dynamics model is reconstructed by an identifier neural network (INN) using the input and output data. The near-optimal event-based controls and time-based disturbances are designed by training a critic neural network (CNN). With the aid of the designed event-triggered mechanism (ETM), the needless computing and communication actions of the system signals have been reduced so as to save computing/communication resources. Meanwhile, to remove the persistence of excitation (PE) condition, the historical and current data are utilized to construct a modified tuning law of CNN. Theoretically, the uniform ultimate boundedness (UUB) properties of the system states and the critic weights errors are proved by Lyapunov approach. Moreover, the Zeno behavior is proved to be excluded under the designed triggering condition. Finally, the convergence and performance of the online method are verified by simulating a representative example.

In the field of dynamic system identification and prediction, linear models (e.g., autoregressive models), nonlinear models (namely, neural networks models), and hybrid predictors (HPs) that are a hybridization of linear and nonlinear models have been proposed in the past. However, they are not completely free from limitations: they exhibit difficulties to describe high-order nonlinear relations between input and output variables. In this study, we propose fuzzy reinforced polynomial neural networks (FRPNNs), which are polynomial neural network architecture-based on fuzzy reinforced polynomial neurons (FRPNs) to overcome this limitation. The proposed FRPNs that consist of approximation part (AP) and compensation part (CP) arise as novel HPs. Here the CP for modeling nonlinear patterns can be regarded as forming the reinforced part for the AP that aims at capturing linear patterns, while AP is the linear polynomial neuron used in the conventional polynomial neural networks. In some sense, the overall FRPNNs are essentially generalized polynomial neural network architecture with novel HPs. The parameters considered in the design of the proposed fuzzy reinforced polynomial neural networks are optimized with the aid of the particle swarm optimization (PSO). The performance of FRPNNs is discussed involving time series and system identification datasets. Experimental results demonstrate that the proposed FRPNNs achieve at most the accuracy of 43.6% higher in comparison with the accuracy produced by some classical models reported in the literature.

Aiming at tracking control with bounded torque inputs of the flexible-joint robot manipulators, we propose a generalized saturated adaptive controller based on backstepping control, singular perturbation decoupling and neural networks. First, by using the singular perturbation theory, the full-order rigidflexible dynamics of the robot manipulator is decoupled into a slow subsystem and a fast subsystem. Second, saturated sub-controller by backstepping method is proposed for the slow subsystem, where the projection-type parameter adaptation and a class of saturation functions are applied to make the torque inputs bounded, and a saturated neural network approximator is involved to simplify the control law and to compensate for the uncertain nonlinearity. Third, for fast subsystem, a new filtered tracking error of the elastic torque is used in the fast control law to make the boundary layer subside quickly. In addition, explicit but strict stability analysis is given for the system. Finally, comparisons indicate that the proposed controller results in a more satisfactory tracking performance with keeping the control inputs bounded within the given range all the time and superior anti-disturbance capability.