Parallel Algorithms for Integrated Structural/Control Optimization

Abstract

Optimization of combined structural and control systems is a complex problem requiring an inordinate amount of computer-processing time, especially the solution of the eigenvalue problem of a general unsymmetric square real matrix with complex eigenvalues and eigenvectors, which is frequently used in such problem. The few algorithms presented in the literature thus far have been applied to small structures with a few members and controllers only. Parallel processing on new-generation multiprocessor computers provides an opportunity to solve large-scale problems. In this paper, the integrated structural and control optimization problem is formulated by including constraints on displacements, stresses, and closed-loop eigenvalues and the corresponding damping factors. Then, parallel algorithms are presented for integrated optimization of structures on shared-memory multiprocessors such as the CRAY YMP 8/864 supercomputer. In particular, parallel algorithms are presented for the solution of complex eigenvalue problems encountered in structural control problems using the method of matrix iteration for dominant eigenvalue(s). The solution is divided into two parts. The first part is the iteration for dominant eigenvalue(s) and the corresponding eigenvector(s) and the second part is the reduction of the matrix to obtain the smaller eigenvalue(s) and the corresponding eigenvector(s).