An imbedded initialization of Newton's algorithm for matrix Riccati equation

✍ Scribed by M. Jamshidi

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 317 KB
• Volume: 14
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(78)90023-7

✦ Synopsis

An effective numerical computation of the steadystate Riccati matrix is based on the successive solutions of a Lyapunov equation using Newton's method. The requirements of this algorithm are an initial stabilizing matrix and the numerical solution of the associated Lyapunov equation. Computationally, the first requirement is the more influencing factor in solving the Riccati equation with reasonable accuracy and speed. In this paper an initial matrix, based on the parameter imbedded solution of the Riccati equation, is introduced for the Newton's algorithm. The imbedding Newton algorithm has been applied to a variety of system, both stable and unstable as well as high-dimensional, A matrices, one of which is reported here. The proposed modification has improved the required CPU time of previous initialization schemes by as much as a factor of 6 times for the same order of accuracy.