Riccati equations for stable well-posed linear systems: The generic case
| Autor: | Ruth F. Curtain |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2003 |
| Předmět: |
OPERATORS
Control and Optimization spectral factorizations Resolvent set Popov function FEEDBACK Applied Mathematics Mathematical analysis Linear-quadratic regulator Optimal control Linear-quadratic-Gaussian control Bounded operator Algebraic Riccati equation optimal control weakly regular linear systems Bounded function ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Riccati equation Applied mathematics well-posed linear systems QUADRATIC OPTIMAL-CONTROL Riccati equations Mathematics |
| Zdroj: | SIAM Journal on Control and Optimization, 42(5), 1681-1702. SIAM PUBLICATIONS |
| ISSN: | 0363-0129 |
| Popis: | Under the generic assumption that zero is in the resolvent set of the generator, we show that the optimal control problem for a stable well-posed linear system is equivalent to a control problem for its reciprocal system which has bounded generating operators. Consequently, the operator X that defines the optimal cost satisfies a Riccati equation with bounded operators. Previous results needed various regularity assumptions to obtain X as a solution to a Riccati equation resembling that in the finite-dimensional theory. |
| Databáze: | OpenAIRE |
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