Abstract
This article is devoted to the development of methodological supports and experimental software tools for accuracy analysis and information processing in control stochastic systems (CStS) with complex shock disturbances (ShD) by means of wavelet Haar–Galerkin technologies. Basic new results include methods and algorithms of stochastic covariance analysis and modeling on the basis of the Galerkin method and wavelet expansion for linear, linear with parametric noises, and quasilinear CStS with ShD. Results are illustrated by an information-control system at ShD. New stochastic effects accumulation for systematic and random errors are detected and investigated.
Highlights
Control stochastic systems (CStS) described by nonstationary linear stochastic differential equations (SDE) in the Ito sense with parametric noises are the most adequate models at single shock disturbance (ShD) and Gaussian and non-Gaussian multi-ShD
Nowadays wavelet methods are intensively applied to the problem of deterministic and stochastic numerical analysis and modeling
In the past few decades, a broad range of numerical methods based on Haar wavelet methods achieved great success [5]
Summary
Control stochastic systems (CStS) described by nonstationary linear stochastic differential equations (SDE) in the Ito sense with parametric noises are the most adequate models at single shock disturbance (ShD) and Gaussian and non-Gaussian multi-ShD. In the past few decades, a broad range of numerical methods based on Haar wavelet methods achieved great success [5]. These methods are simple in sense versatility and flexibility and possess less computational cost for accuracy problems. In [25,26], a combination of Haar wavelets and the Galerkin method [22] numerical solution of linear equations were presented. Development of the Haar–Galerkin method and experimental software tools for accuracy analysis of CStS at single ShD is given in [19,20]. Let us consider modeling the wavelet Haar–Galerkin methodology and experimental software tools for covariance accuracy analysis of CStS at complex multi-ShD
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