Computational structural mechanics. Optimal control and semi-analytical method for PDE

Abstract

Based on the generalized variational principle the analysis of a substructural chain is considered, and the 1:1 relationship between the structural analysis problem and the linear quadratic optimal control problem is then introduced. Hence, the algebraic Riccati equation can be solved in two ways; the upper-bound and lower-bound iterative methods. The theory and methods of structural analysis problems can then be transferred to the linear quadratic optimal control problems. As to the continuous coordinate, and/or continuous-time problems, it can be shown that the linear quadratic control problem also corresponds to the semi-analytical method of the elliptic partial differential equation. It is hoped that the unified method of these disciplines will lead to further progress.