Sharif Digital Repository

Predicting future behavior of chaotic time series and systems is a challenging area in the literature of nonlinear systems. The prediction accuracy of chaotic time series is extremely dependent on the model and the learning algorithm. In addition, the generalization property of the proposed models trained by limited observations is of great importance. In the past two decades, singular or descriptor systems and related fuzzy descriptor models have been the subjects of interest due to their many practical applications in modeling complex phenomena. In this study fuzzy descriptor models, as a more recent neurofuzzy realization of locally linear descriptor systems, which have led to the... 

Singular spectrum analysis (SSA) is a well-studied approach in signal processing. SSA has originally been designed to extract information from short noisy chaotic time series and to enhance the signal-to-noise ratio. SSA is good for offline applications; however, many applications, such as modelling, analysis, and prediction of time-varying and non-stationary time series, demand for online analysis. This study introduces a recursive algorithm called recursive SSA as a modification to regular SSA for dynamic and online applications. The proposed method is based on eigenvector matrix perturbation approach. After recursively calculating the covariance matrix of the trajectory matrix, R-SSA... 

In this paper, the problem of statistical reconstruction and prediction of chaotic systems with unknown governing equations using stochastic Markov models is investigated. Using the time series of only one measurable state, an algorithm is proposed to design any orders of Markov models and the approach is state transition matrix extraction. Using this modeling, two goals are followed: first, using the time series, statistical reconstruction is performed through which the probability density and conditional probability density functions are reconstructed; and second, prediction is performed. For this problem, some estimators are required and here the maximum likelihood and the conditional...