Robust Parallel Algorithms for Solution of Riccati Equation

Abstract

Robust and efficient parallel-vector algorithms are presented for the solution of the Riccati equations encountered in optimal control problems on shared-memory multiprocessor machines. The algorithms have been implemented on a Cray YMP 8/8128 and applied to three large problems resulting from a continuous bridge structure, a 21-story space truss structure, and a 12-story space moment-resisting building structure. Efficiency of the algorithms is presented in terms of millions of floating point operations per second (MFLOPS) and the speedup. The MFLOPS for the largest example resulting from the 12-story space frame structure is a high 206.0. The speedup due to parallel processing only (for the same example), using seven processors, is 6.33. When vectorization is combined with parallel processing a very significant speedup of 54.4 is obtained using seven processors. The algorithms developed in this research find applications in the complex integrated control/structural optimization problem. Further, the writers are currently using them to develop large adaptive/smart structures.