|
| << vorige | volgende >> |
Tijdschrift beschrijving
Alle jaargangen van het bijbehorende tijdschrift
Alle afleveringen van het bijbehorende jaargang
Alle artikelen van de bijbehorende aflevering
Details van artikel 5 van 14 gevonden artikelen
| Titel: |
Homotopy methods for solving the optimal projection equations for the H2 reduced order model problem |
| Auteur: |
Zigic, Dragan Watson, Layne T. Collins, Emmanuel G. Bernstein, Dennis S. |
| Verschenen in: |
International journal of control |
| Paginering: | Jaargang 56 (1992) nr. 1 pagina's 173-191 |
| Jaar: |
1992 |
| Inhoud: |
The optimal projection approach to solving the H2 reduced order model problem produces two coupled, highly nonlinear matrix equations with rank conditions as constraints. Owing to the resemblance of these equations to standard matrix Lyapunov equations, they are called modified Lyapunov equations. The algorithms proposed herein utilize probability-one homotopy theory as the main tool. It is shown that there is a family of systems (the homotopy) that makes a continuous transformation from some initial system to the final system. With a carefully chosen initial problem, a theorem guarantees that all the systems along the homotopy path will be asymptotically stable, controllable and observable. One method, which solves the equations in their original form, requires a decomposition of the projection matrix using the Drazin inverse of a matrix. It is shown that the appropriate inverse is a differentiable function. An effective algorithm for computing the derivative of the projection matrix that involves solving a set of Sylvester equations is given. Another class of methods considers the equations in a modified form, using a decomposition of the pseudogramians based on a contragredient transformation. Some freedom is left in making an exact match between the number of equations and the number of unknowns, thus effectively generating a family of methods. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 5 van 14 gevonden artikelen
| << vorige | volgende >> |