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Newton's Method with Exact Line Search for Solving the Algebraic Riccati Equation (1995)
| Content Provider | CiteSeerX |
|---|---|
| Author | Benner, Peter Byers, Ralph |
| Abstract | This paper studies Newton's method for solving the algebraic Riccati equation combined with an exact line search. Based on these considerations we present a Newton--like method for solving algebraic Riccati equations. This method can improve the sometimes erratic convergence behavior of Newton's method. 1 Introduction We study the generalized continuous--time algebraic Riccati equation (CARE) 0 = R(X) = C T QC +A T XE + E T XA \Gamma (B T XE + S T C) T R \Gamma1 (B T XE + S T C) (1) Here A; E; X 2 IR n\Thetan , B 2 IR n\Thetam , R = R T 2 IR m\Thetam , Q = Q T 2 IR p\Thetap , C 2 IR p\Thetan , and S 2 IR p\Thetam . This equation arises frequently in control problems. We will assume that E and R are nonsingular and Q S S T R 0, where M 0 denotes positive semidefinite matrices M . Often, the desired solution X is stabilizing in the sense that the eigenvalues of the matrix pencil E \Gamma (A \Gamma BR \Gamma1 (B T XE + S T C)) have negati... |
| File Format | |
| Publisher Date | 1995-01-01 |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
