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For a class of stochastic nonlinear systems in pure-feedback form with dead-zone input and multiple time-varying delays, a novel neural network (NN)-based adaptive control approach is presented in this paper through the use of backstepping approach and dynamic surface technique. By choosing proper Lyapunov–Krasovskii functionals, utilizing the characteristic of hyperbolic tangent functions and adopting the function separation technique, difficulties of controller design that introduced by the time-varying delays can be dealt with properly. Moreover, all unknown nonlinear functions are lumped together and approximated by the NN. Additionally, any information over the boundedness of dead-zone parameters is not needed in the process of controller design. The control scheme proposed in this paper ensures the boundedness in probability of all signals in the closed-loop system, besides, excellent performance of arbitrarily small tracking error will be achieved by selecting control parameters appropriately. At last, two numerical simulation examples are provided to verify the validity of the designed algorithm. [ABSTRACT FROM AUTHOR]

This paper establishes an approximate optimal critic learning algorithm based on single neural network (NN) policy iteration (PI) aiming at solving for continuous-time (CT) 2-player zero-sum games (ZSGs). In fact, we have to face the problem that the errors will disturb the dynamics and in turn identifying dynamics will generate errors. In order to prevent the effect of errors, in this paper, a single NN-based online PI algorithm is developed for the CT system, which is disturbed nonlinear ZSG. With plenty of online data, the Hamilton–Jacobi–Isaacs equation can be solved without complete dynamics. Then by the least-squares method, we can obtain the NN weights. Moreover, in the process of dealing with the undisturbed system, we find the way that obtains NN weights in this paper is equal to the way that obtains the optimal solution by the Gauss–Newton method. Based on the convergence of the Gauss–Newton method, we can efficiently obtain the optimal controller for the undisturbed system by utilizing online data. After getting the controller of the undisturbed system, it is time to take disturbance into consideration, so that we design a robust control pair to overcome the disturbance. In order to demonstrate the effectiveness of this algorithm, we design a set of simulations. The results verify that we can solve the disturbed nonlinear ZSG by this algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive dynamic programming (ADP) algorithm is developed for the infinite-horizon ($H_{\infty}$) optimal control problems with unknown continuous-time (CT) nonlinear systems subject to external disturbances. To facilitate the implementation of the algorithm, generalized fuzzy hyperbolic models (GFHMs) are utilized to establish an identifier–critic architecture, where the identifier is designed to reconstruct the unknown system dynamics, and the GFHM-based critic network is employed to approximate the value functions. The CT $H_{\infty}$ optimal control issue is converted into a two-player zero-sum game and the corresponding Hamilton–Jacobi–Isaacs equation is derived. The learning procedure of the critic design is adaptively implemented with the help of the reconstructed model, thus the requirement of the complete system dynamics is relaxed. Furthermore, by the means of Lyapunov direct method, the uniform ultimate boundedness stability analysis of the closed-loop control system is explicitly provided. Finally, to compare the control performances and disturbance attenuation properties of the proposed method and the existing ADP algorithms, two numerical examples are given. [ABSTRACT FROM AUTHOR]

In this paper, a novel event-sampled robust optimal controller is proposed for a class of continuous-time constrained-input nonlinear systems with unknown dynamics. In order to solve the robust optimal control problem, an online data-driven identifier is established to construct the system dynamics, and an event-sampled critic-only adaptive dynamic programming method is developed to replace the conventional time-driven actor–critic structure. The designed online identification method runs during the solving process and is not applied as a priori part for the solutions, which simplifies the architecture and reduces computational load. The proposed robust optimal control algorithm tunes the parameters of critic-only neural network (NN) by event-triggering condition and runs in a plug-n-play framework without system functions, where fewer transmissions and less computation are required as all the measurements received simultaneously. Based on the novel design, the stability of system and the convergence of critic NN are demonstrated by Lyapunov theory, where the state is asymptotically stable and weight error is guaranteed to be uniformly ultimately bounded. Finally, the applications in a basic nonlinear system and the complex rotational–translational actuator problem demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the data-based optimal control for a class of networked industrial processes with a double-layer architecture. Without knowing the dynamics of subsystems at the device layer, the index prediction function is constructed via the input/output signals, and radial basis function neural networks. The tuning laws for the index prediction function are obtained through the optimal control strategy. Then, by treating the network-induced phenomenon as random round-trip time delay and introducing the predictive algorithm, the compensation scheme is designed at the operation layer to dynamically decompose the setpoints. Finally, two simulation examples are given to further illustrate the effectiveness of the proposed compensation strategy. [ABSTRACT FROM AUTHOR]

Neural networks (NNs) have numerous applications to online processes, but the problem of stability is rarely discussed. This is an extremely important issue because, if the stability of a solution is not guaranteed, the equipment that is being used can be damaged, which can also cause serious accidents. It is true that in some research papers this problem has been considered, but this concerns continuous-time NN only. At the same time, there are many systems that are better described in the discrete time domain such as population of animals, the annual expenses in an industry, the interest earned by a bank, or the prediction of the distribution of loads stored every hour in a warehouse. Therefore, it is of paramount importance to consider the stability of the discrete-time NN. This paper makes several important contributions. 1) A theorem is stated and proven which guarantees uniform stability of a general discrete-time system. 2) It is proven that the backpropagation (BP) algorithm with a new time-varying rate is uniformly stable for online identification and the identification error converges to a small zone bounded by the uncertainty. 3) It is proven that the weights' error is bounded by the initial weights' error, i.e., overfitting is eliminated in the proposed algorithm. 4) The BP algorithm is applied to predict the distribution of loads that a transelevator receives from a trailer and places in the deposits in a warehouse every hour, so that the deposits in the warehouse are reserved in advance using the prediction results. 5) The BP algorithm is compared with the recursive least square (RLS) algorithm and with the Takagi–Sugeno type fuzzy inference system in the problem of predicting the distribution of loads in a warehouse, giving that the first and the second are stable and the third is unstable. 6) The BP algorithm is compared with the RLS algorithm and with the Kalman filter algorithm in a synthetic example. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy logic system (FLS) cascaded with neural network, type-2 fuzzy neural network (T2FNN), is presented in this paper to handle uncertainty with dynamical optimal learning. A T2FNN consists of a type-2 fuzzy linguistic process as the antecedent part, and the two-layer interval neural network as the consequent part A general T2FNN is computational-intensive due to the complexity of type 2 to type 1 reduction. Therefore, the interval T2FNN is adopted in this paper to simplify the computational process. The dynamical optimal training algorithm for the two-layer consequent part of interval T2FNN is first developed. The stable and optimal left and right learning rates for the interval neural network, in the sense of maximum error reduction, can be derived for each iteration in the training process (back propagation). It can also be shown both learning rates cannot be both negative. Further, due to variation of the initial MF parameters, i.e., the spread level of uncertain means or deviations of interval Gaussian MFs, the performance of back propagation trailing process may be affected. To achieve better total performance, a genetic algorithm (GA) is designed to search optimal spread rate for uncertain means and optimal learning for the antecedent part. Several examples are fully illustrated. Excellent results are obtained for the truck backing-up control and the identification of nonlinear system, which yield more improved performance than those using type-i FNN. [ABSTRACT FROM AUTHOR]

This paper presents a controller integrity monitoring method for a class of second-order nonlinear uncertain systems incorporating neural network-based adaptive control algorithms. The adaptive neural network model is employed to ensure robust tracking performance in the presence of certain modeling uncertainty under consideration during the offline controller design process. Based on Lyapunov stability analysis, an online controller integrity monitoring scheme is developed to detect the occurrence of controller software/algorithm faults and unanticipated physical component faults, which may lead to unstable learning behaviors and malfunctions of the adaptive controller. Adaptive thresholds for detecting controller malfunctions are derived, ensuring the robustness with respect to modeling uncertainty and neural network approximation error. Additionally, the detectability conditions are investigated, characterizing the class of detectable software faults and unanticipated physical faults. An upper bound on the fault detection time is also established. Simulation results are shown to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Bounding ellipsoid (BE) algorithms offer an attractive alternative to traditional training algorithms for neural networks, for example, backpropagation and least squares methods. The benefits include high computational efficiency and fast convergence speed. In this paper, we propose an ellipsoid propagation algorithm to train the weights of recurrent neural networks for nonlinear systems identification. Both hidden layers and output layers can be updated. The stability of the BE algorithm is proven. [ABSTRACT FROM AUTHOR]

This paper presents the design and stability analysis of a sampled-data neural-network-based control system. A continuous-time nonlinear plant and a sampled-data three-layer fully connected feedforward neural-network-based controller are connected in a closed loop to perform the control task. Stability conditions will be derived to guarantee the closed-loop system stability. Linear-matrix-inequality- and genetic-algorithm-based approaches will be employed to obtain the largest sampling period and the connection weights of the neural network subject to the considerations of the system stability and performance. An application example will be given to illustrate the design procedure and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper proposes a wavelet adaptive backstepping control (WABC) system for a class of second-order nonlinear systems. The WABC comprises a neural backstepping controller and a robust controller. The neural backstepping controller containing a wavelet neural network (WNN) identifier is the principal controller, and the robust controller is designed to achieve L2 tracking performance with desired attenuation level. Since the WNN uses wavelet functions, its learning capability is superior to the conventional neural network for system identification. Moreover, the adaptation laws of the control system are derived in the sense of Lyapunov function and Barbalat's lemma, thus the system can be guaranteed to be asymptotically stable. The proposed WABC is applied to two nonlinear systems, a chaotic system and a wing-rock motion system to illustrate its effectiveness. Simulation results verify that the proposed WABC can achieve favorable tracking performance by incorporating of WNN identification, adaptive backstepping control, and L2 robust control techniques. [ABSTRACT FROM AUTHOR]

A stable neural network (NN)-based observer for general multivariable nonlinear systems is presented in this paper. Unlike most previous neural network observers, the proposed observer uses a nonlinear-in-parameters neural network (NLPNN). Therefore, it can be applied to systems with higher degrees of non- linearity without any a priori knowledge about system dynamics. The learning rule for the neural network is a novel approach based on the modified backpropagatfon (BP) algorithm. An e-modification term is added to guarantee robustness of the observer. No strictly positive real (SPR) or any other strong assumption is imposed on the proposed approach. The stability of the recurrent neural network observer is shown by Lyapunov's direct method. Simulation results for a flexible-joint manipulator are presented to demonstrate the enhanced performance achieved by utilizing the proposed neural network observer. [ABSTRACT FROM AUTHOR]