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This work focuses on developing a forecasting model for the nonlinear system with herding. Firstly, for clear presentation of the mechanism of herding behavior, a concept called intermittent positive feedback is defined. The mathematical expression of intermittent positive feedback is formulated in terms of dead-zone functions with the beginning and ending thresholds in the positive and negative directions. Then a dynamic surrogate based on the intermittent positive feedback multi-dimensional Taylor network is established, and a method for identifying its parameters is proposed. Multi-dimensional Taylor network module simulates the long-term trends of time series. Subsequently, an optimization model based on the alternating iteration of the parameters is developed to enhance the forecast accuracy of the intermittent positive feedback part. Simulation results demonstrate that the forecasting effect of the proposed modeling method is superior to that of conventional non-mechanism data-based surrogates for herding behavior. [ABSTRACT FROM AUTHOR]

In view of the difficulty of modelling time-varying nonlinear systems, a multidimensional Taylor network (MTN) model based on dynamic characteristic clustering is proposed to establish an online time series forecasting model. The construction method of a MTN, the definitions of the dynamic characteristics, and their similarity criteria are discussed. Specific steps of the MTN online model, based on dynamic clustering, are given. A practical example is presented to demonstrate how the proposed method works in a real application, and its effectiveness is verified. [ABSTRACT FROM AUTHOR]

In this study, an adaptive predictive control approach based on the multi-dimensional Taylor network (MTN) is proposed for the real-time tracking control of single-input single-output nonlinear systems with input time-delay. Two MTNs are used to implement the accurate tracking control. First, to compensate for the influence of time-delay, MTN is taken as a predictor and the damped recursive least squares algorithm is used as its online learning algorithm. Second, a feed-forward MTN controller is developed on the basis of the proportional–integral–derivative controller, and the closed-loop errors between the reference input and the system output are directly chosen to be the MTN controller's inputs. The back propagation algorithm is introduced for its learning which can update its weights online at stable learning rate by the errors caused by the system's uncertain factors. Convergence and stability analysis are given to guarantee the performance of our proposed approach. Finally, two examples are given to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]