An output error bound for time-limited balanced truncation
| Autor: | Patrick Kürschner, Martin Redmann |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
Technology General Computer Science Computational complexity theory Linear systems 010103 numerical & computational mathematics 02 engineering and technology Interval (mathematics) Mathematical proof 01 natural sciences 020901 industrial engineering & automation Automation & Control Systems Time-limited balanced truncation SYSTEMS Order (group theory) Applied mathematics Time domain 0101 mathematics Electrical and Electronic Engineering Time-limited Gramians Mathematics Model order reduction Partial differential equation Science & Technology Model reduction Mechanical Engineering Operations Research & Management Science Singular value Control and Systems Engineering Error bound |
| Zdroj: | Systems & Control Letters |
| Popis: | Model order reduction (MOR) is often applied to spatially-discretized partial differential equations to reduce their order and hence decrease computational complexity. A reduced system can be obtained, e.g., by time-limited balanced truncation, a method that aims to construct an accurate reduced order model on a given finite time interval [ 0 , T ] . This particular balancing related MOR technique is studied in this paper. An L T 2 -error bound based on the truncated time-limited singular values is proved and is the main result of this paper. The derived error bound converges (as T → ∞ ) to the well-known H ∞ -error bound of unrestricted balanced truncation, a scheme that is used to construct a good reduced system on the entire time line. The techniques within the proofs of this paper can also be applied to unrestricted balanced truncation so that a relatively short time domain proof of the H ∞ -error bound is found here. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|