Exact linear modeling using Ore algebras

Exact linear modeling using Ore algebras

Linear exact modeling is a problem coming from system identification: Given a set of observed trajectories, the goal is find a model (usually, a system of partial differential and/or difference equations) that explains the data as precisely as possible. The case of operators with constant coefficients is well studied and known in the systems theoretic literature, whereas the operators with vary...

Effective algebraic analysis approach to linear systems over Ore algebras

Exact linear modeling with polynomial coefficients

Given a finite set of polynomial, multivariate, and vector-valued functions, we show that their span can be written as the solution set of a linear system of partial differential equations (PDE) with polynomial coefficients. We present two different but equivalent ways to construct a PDE system whose solution set is precisely the span of the given trajectories. One is based on commutative algeb...

Blast vibration modeling using linear superposition method

A linear superposition method was used for modeling the time history of the production blast vibrations and optimizing the blast sequence to reduce vibration levels in Sar-Cheshmeh copper mine, Kerman, Iran. A single-hole blast for modeling and two double-hole blasts with time delays of 25 and 65 ms between two holes for modeling validation were carried out. The generated vibrations were measur...

Linear Control Systems over Ore Algebras: Effective Algorithms for the Computation of Parametrizations

In this paper, we study linear control systems over Ore algebras. Within this mathematical framework, we can simultaneously deal with different classes of linear control systems such as time-varying ordinary differential systems, differential time-delay systems, partial differential equations, multidimensional discrete systems, etc. We give effective algorithms which check whether or not a line...