Multidimensional time series (MTS) has the unique characteristics of multidimensionality and multifeature, so it becomes particularly important when choosing a prediction model. Therefore, this article proposes a novel broad echo state network (Broad-ESN) based on radical activation function (RB-ESN). First, a radical activation function is proposed to solve the problem of gradient disappearing in the iterative process and is more conducive to dealing with complex data patterns. Second, the sliding window is used to extract the features of MTS. The number of reservoirs is determined by the number of features. Third, by using Cubic chaotic mapping to initialize the pied kingfisher optimizer (PKO) population, the search space can be effectively expanded, and high-quality random sequences can be generated. Then, the exponential spiral equation is used to optimize the position update equation of the pied kingfisher, which solves the problem of local optimization. Finally, the results show that the model proposed in this article is significantly superior to other models in forecasting performance, with high prediction accuracy and low error.

This paper studies the fuzzy Hinfinfilter design problem for signal estimation of nonlinear discrete-time systems with multiple time delays and unknown bounded disturbances. First, the Takagi-Sugeno (T-S) fuzzy model is used to represent the state-space model of nonlinear discrete-time systems with time delays. Next, we design a stable fuzzy Hinfinfilter based on the T-S fuzzy model, which guarantees asymptotic stability and a prescribed Hinfinindex for the filtering error system, irrespective of the time delays and uncertain disturbances. A sufficient condition for the existence of such a filter is established by using the linear matrix inequality (LMI) approach. The proposed LMI problem can be efficiently solved with global convergence guarantee using convex optimization techniques such as the interior point algorithm. Simulation examples are provided to illustrate the design procedure of the present method.