State controllability computation technique for linear time‐varying systems by using Taylor series approximation

Abstract

This article presents a technique to determine the controllability Grammian matrix (CGM) for linear timevarying systems by using truncated Taylor polynomial vector and the operational matrix of integration. An important property of this algorithm is that it starts by integrating the Lyapunov differential matrix equation in terms of the CGM. However, the algorithm does not use the mathematical integration processes actually, but uses the truncated Taylor polynomial vector and the operational matrix of integration. Thus, the problem is reduced to solving a linear set of algebraic equations with constant coefficients consisting of the Taylor polynomial constant coefficients of each of the CGM elements. Numerical results and error curves are given to illustrate the improvements achieved by the proposed algorithm.

Bayesian prediction of bridge extreme stresses based on DLTM and monitoring coupled data

“…Therefore, only the local data points near the any given point θ 0 can be used. Assume that f ( θ ) has the ( p + 1)-order derivative at θ 0 , then f ( θ ) can be commonly expanded at θ 0 with p -order Taylor series approximation, 51 namely…”