Identification method for a class of periodic discrete-time dynamic nonlinear systems based on Sinusoidal ESN

Dual Heuristic Programming for Optimal Control of Continuous-Time Nonlinear Systems Using Single Echo State Network

This article presents an improved online adaptive dynamic programming (ADP) algorithm to solve the optimal control problem of continuous-time nonlinear systems with infinite horizon cost. The Hamilton-Jacobi-Bellman (HJB) equation is iteratively approximated by a novel critic-only structure which is constructed using the single echo state network (ESN). Inspired by the dual heuristic programming (DHP) technique, ESN is designed to approximate the costate function, then to derive the optimal controller. As the ESN is characterized by the echo state property (ESP), it is proved that the ESN can successfully approximate the solution to the HJB equation. Besides, to eliminate the requirement for the initial admissible control, a new weight tuning law is designed by adding an alternative condition. The stability of the closed-loop optimal control system and the convergence of the out weights of the ESN are guaranteed by using the Lyapunov theorem in the sense of uniformly ultimately bounded (UUB). Two simulation examples, including linear system and nonlinear system, are given to illustrate the availability and effectiveness of the proposed approach by comparing it with the polynomial neural-network scheme.

New Varying-Parameter ZNN Models With Finite-Time Convergence and Noise Suppression for Time-Varying Matrix Moore-Penrose Inversion

This article aims to solve the Moore-Penrose inverse of time-varying full-rank matrices in the presence of various noises in real time. For this purpose, two varying-parameter zeroing neural networks (VPZNNs) are proposed. Specifically, VPZNN-R and VPZNN-L models, which are based on a new design formula, are designed to solve the right and left Moore-Penrose inversion problems of time-varying full-rank matrices, respectively. The two VPZNN models are activated by two novel varying-parameter nonlinear activation functions. Detailed theoretical derivations are presented to show the desired finite-time convergence and outstanding robustness of the proposed VPZNN models under various kinds of noises. In addition, existing neural models, such as the original ZNN (OZNN) and the integration-enhanced ZNN (IEZNN), are compared with the VPZNN models. Simulation observations verify the advantages of the VPZNN models over the OZNN and IEZNN models in terms of convergence and robustness. The potential of the VPZNN models for robotic applications is then illustrated by an example of robot path tracking.

Nonsynaptic Error Backpropagation in Long-Term Cognitive Networks

We introduce a neural cognitive mapping technique named long-term cognitive network (LTCN) that is able to memorize long-term dependencies between a sequence of input and output vectors, especially in those scenarios that require predicting the values of multiple dependent variables at the same time. The proposed technique is an extension of a recently proposed method named short-term cognitive network that aims at preserving the expert knowledge encoded in the weight matrix while optimizing the nonlinear mappings provided by the transfer function of each neuron. A nonsynaptic, backpropagation-based learning algorithm powered by stochastic gradient descent is put forward to iteratively optimize four parameters of the generalized sigmoid transfer function associated with each neuron. Numerical simulations over 35 multivariate regression and pattern completion data sets confirm that the proposed LTCN algorithm attains statistically significant performance differences with respect to other well-known state-of-the-art methods.

Hybrid Regularized Echo State Network for Multivariate Chaotic Time Series Prediction

Multivariate chaotic time series prediction is a hot research topic, the goal of which is to predict the future of the time series based on past observations. Echo state networks (ESNs) have recently been widely used in time series prediction, but there may be an ill-posed problem for a large number of unknown output weights. To solve this problem, we propose a hybrid regularized ESN, which employs a sparse regression with the L₁/2 regularization and the L₂ regularization to compute the output weights. The L₁/2 penalty shows many attractive properties, such as unbiasedness and sparsity. The L₂ penalty presents appealing ability on shrinking the amplitude of the output weights. After the output weights are calculated, the input weights, internal weights, and output weights are fine-tuning by a Hessian-free optimization method-conjugate gradient backpropagation algorithm. The fine-tuning helps to bubble up the input information toward the output layer. Besides, the largest Lyapunov exponent is used to calculate the predictable horizon of a chaotic time series. Experimental results on benchmark and real-world datasets show that our proposed method is superior to other ESN-based models, as sparser, smaller-absolute-value, and more informative output weights are obtained. All of the predictions within the predictable horizon of the proposed model are accurate.