Name
Title | ||
|---|---|---|
Model Boundary Approximation Method as a Unifying Framework for Balanced Truncation and Singular Perturbation Approximation. |
Abstract | ||
|---|---|---|
We show that two widely accepted reduction techniques, Balanced Truncation and Balanced Singular Perturbation Approximation, can be derived as limiting approximations of a carefully constructed parameterization of Linear Time Invariant (LTI) systems by employing the Model Boundary Approximation Method (MBAM), a recent development in the Physics literature. This unifying framework of these popular reduction techniques shows that Balanced Truncation and Balanced Singular Perturbation Approximation each correspond to a particular boundary point on a the model manifold, which is associated with the specific choice of parameterization and initial condition, and is embedded in a sample space of measured outputs, which can be chosen arbitrarily, provided that the number of samples exceeds the number of parameters. We also show that MBAM provides a novel way to interpolate between Balanced Truncation and Balanced Singular Perturbation Approximation, by exploring the set of approximations on the boundary of the manifold between the elements that correspond to the two reduction techniques; this allows for alternative approximations of a given system to be found that may be better under certain conditions. The work herein suggests similar types of approximations may be obtainable in topologically similar places (i.e. on certain boundaries) on the manifold of nonlinear systems if analogous parameterizations can be achieved, therefore extending these widely accepted reduction techniques to nonlinear systems. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1109/TAC.2019.2908523 | IEEE Transactions on Automatic Control |
Keywords | Field | DocType |
Manifolds,Linear systems,Reduced order systems,Brain modeling,Perturbation methods,Complexity theory,Data models | Applied mathematics,LTI system theory,Discrete mathematics,Nonlinear system,Parametrization,Boundary (topology),Singular perturbation,Initial value problem,Sample space,Mathematics,Manifold | Journal |
Volume | Issue | ISSN |
64 | 11 | 0018-9286 |
Citations | PageRank | References |
2 | 0.41 | 15 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Philip E. Pare | 1 | 14 | 7.53 |
| David Grimsman | 2 | 7 | 1.89 |
| Alma Teao Wilson | 3 | 2 | 0.41 |
| Mark K. Transtrum | 4 | 13 | 2.68 |
| Sean Warnick | 5 | 198 | 25.76 |