Analysis of an iteration method for the algebraic Riccati equation. (English) Zbl 1339.15010
Summary: We consider a recently published method for solving algebraic Riccati equations. We present a new perspective on this method in terms of the underlying linear-quadratic optimal control problem: we prove that the matrix obtained by this method expresses the optimal cost for a projected optimal control problem. The projection is determined by the so-called shift parameters of the method. Our representation in terms of the optimal control problem gives rise to a simple and very general convergence analysis.
MSC:
| 15A24 | Matrix equations and identities |
| 49N10 | Linear-quadratic optimal control problems |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 65F30 | Other matrix algorithms (MSC2010) |
| 49M30 | Other numerical methods in calculus of variations (MSC2010) |
| 93B52 | Feedback control |
| 65K10 | Numerical optimization and variational techniques |
Keywords:
algebraic Riccati equation; ADI iteration; numerical method in control theory; linear-quadratic optimal controlReferences:
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