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This paper focuses on the issue of robust stability analysis for recurrent neural networks (RNNs) with leakage delay. By constructing a novel Lyapunov-Krasovskii functional together with the reciprocally convex approach and the free-weighting matrix technique, some less conservative stability criteria in terms of linear matrix inequalities for RNNs are derived. The new contribution of this paper is that a novel delay-partitioning method is proposed, and some new zero equalities are introduced. Finally, several examples are given to demonstrate the effectiveness of the proposed methods. The simulated results reveal that the leakage delay has great influence on the dynamical systems, and it cannot be neglected. [ABSTRACT FROM AUTHOR]

We investigate state estimation for a class of discrete-time recurrent neural networks with leakage delay and time-varying delay. The design method for the state estimator to estimate the neuron states through available output measurements is given. A novel delay-dependent sufficient condition is obtained for the existence of state estimator such that the estimation error system is globally asymptotically stable. Based a novel double summation inequality and reciprocally convex approach, an improved stability criterion is obtained for the error-state system. Two numerical examples are given to demonstrate the effectiveness of the proposed design methods. The simulation results show that the leakage delay has a destabilizing influence on a neural network system. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive critic neural network controller is designed for a class of discrete-time chaotic system. The critic neural network is used to approximate the long-term function. In contrast with the existing results for discrete-time chaotic systems, in this paper, a near optimal control input can be generated when the long-term function is minimized. It is proven that the tracking error, the adaptation laws and the control input are uniformly bounded. A simulation example is employed to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive control algorithm is proposed for a class of robot manipulator systems with unknown functions and dead-zone input by using a reinforcement learning scheme. The parameters of the dead zone are supposed to be unknown but bounded. The unknown functions can be approximated based on the neural networks, which is one part of the reinforcement learning scheme, namely an action network. The other part is called critic network which is used to approximate the reinforcement signal. Then, the prominent advantage of the proposed approach is that an optimal control input can be obtained by using two networks compared with the results of robot manipulator with dead zone: an additional term is given to compensate for the effect of the dead zone, and a special design procedure to solve the difficulties in constructing the controllers and adaptation laws. Based on the Lyapunov analysis theory, all the signals of the closed-loop system are proved to be bounded and the system output can track the reference signal to a bounded compact set. Finally, a simulation example is given to illustrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

In this article, a direct adaptive neural networks control algorithm is presented for a class of SISO discrete-time systems with non-symmetric dead-zone. The property of the dead-zone is discretized. Mean value theorem is used to transform the systems into a special form. The unknown functions in the input–output model are approximated using the radial basis function neural networks. Compared with the results for the discrete non-symmetric dead-zone, this article presents a new algorithm to reduce the computational burden. Lyapunov analysis method is utilized to prove that all the signals in the closed-loop systems are semi-global uniformly ultimately bounded. The tracking error is proved to converge to a small set around the zero. A simulation example provided to illustrate the effectiveness of the control schemes. [ABSTRACT FROM AUTHOR]

A robust adaptive NN output feedback control is proposed to control a class of uncertain discrete-time nonlinear multi-input-multi-output (MIMO) systems. The high-order neural networks are utilized to approximate the unknown nonlinear functions in the systems. Compared with the previous research for discrete-time MIMO systems, robustness of the proposed adaptive algorithm is obvious improved. Using Lyapunov stability theorem, the results show all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero by choosing the design parameters appropriately. [ABSTRACT FROM AUTHOR]

In this paper, a direct adaptive neural network control algorithm based on the backstepping technique is proposed for a class of uncertain nonlinear discrete-time systems in the strict-feedback form. The neural networks are utilized to approximate unknown functions, and a stable adaptive neural network controller is synthesized. The fact that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded is proven and the tracking error can converge to a small neighborhood of zero by choosing the design parameters appropriately. Compared with the previous research for discrete-time systems, the proposed algorithm improves the robustness of the systems. A simulation example is employed to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]