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Recent deterministic learning methods have achieved locally-accurate identification of unknown system dynamics. However, the locally-accurate identification means that the neural networks can only capture the local dynamics knowledge along the system trajectory. In order to capture a broader knowledge region, this article investigates the knowledge fusion problem of deterministic learning, that is, the integration of different knowledge regions along different individual trajectories. Specifically, two kinds of knowledge fusion schemes are systematically introduced: an online fusion scheme and an offline fusion scheme. The online scheme can be viewed as an extension of distributed cooperative learning control to cooperative neural identification for sampled-data systems. By designing an auxiliary information transmission strategy to enable the neural network to receive information learned from other tasks while learning its own task, it is proven that the weights of all localized RBF networks exponentially converge to their common true/ideal values. The offline scheme can be regarded as a knowledge distillation strategy, in which the fused network is obtained by offline training through the knowledge learned from all individual system trajectories via deterministic learning. A novel weight fusion algorithm with low computational complexity is proposed based on the least squares solution under subspace constraints. Simulation studies show that the proposed fusion schemes can successfully integrate the knowledge regions of different individual trajectories while maintaining the learning performance, thereby greatly expanding the knowledge region learned from deterministic learning. [ABSTRACT FROM AUTHOR]

In this paper, based on the sampled-data observer and the deterministic learning theory, a rapid dynamical pattern recognition approach is proposed for univariate time series composed of the output signals of the dynamical systems. Specifically, locally-accurate identification of inherent dynamics of univariate time series is first achieved by using the sampled-data observer and the radial basis function (RBF) networks. The dynamical estimators embedded with the learned knowledge are then designed by resorting to the sampled-data observer. It is proved that generated estimator residuals can reflect the difference between the system dynamics of the training and test univariate time series. Finally, a recognition decision-making scheme is proposed based on the residual norms of the dynamical estimators. Through rigorous analysis, recognition conditions are given to guarantee the accurate recognition of the dynamical pattern of the test univariate time series. The significance of this paper lies in that the difficult problems of dynamical modeling and rapid recognition for univariate time series are solved by incorporating the sampled-data observer design and the deterministic learning theory. The effectiveness of the proposed approach is confirmed by a numerical example and compressor stall warning experiments. • An observer-based recognition approach is proposed for univariate time series. • The challenge of learning dynamical systems from univariate time series is overcome. • Estimators perform recognition tasks, reducing computational complexity. • Average residual norms are used for decisions, which ensures recognition accuracy. [ABSTRACT FROM AUTHOR]

Reliable fault diagnosis (FD) is important to ensure safety in nonlinear engineering systems. Modern engineering systems are often subject to unknown complex nonlinearities and varying operation conditions, therefore, one of the main challenges for FD of nonlinear systems is the robustness against these uncertainties. In this paper, a novel robust FD approach combining the reinforcement learning (RL) and the deterministic learning theory (DLT) is developed for a class of discrete-time nonlinear systems. The DLT is employed to pre-train the neural network (NN) aiming at approximating the unknown nonlinear complexity and obtaining dynamical fault models, then RL techniques are employed to adapt the NN parameters to improve the robustness of fault models. The stability of the learning process is rigorously analyzed using Lyapunov-based methods, and the effectiveness of the presented method is validated by a rotating stall warning experiment based on the data from Beihang University compressor test rig. Experiment results demonstrate that compared with other methods, the proposed method can achieve better performance in lead warning time and robustness. [ABSTRACT FROM AUTHOR]