ml_care_nwt_fac
Continuous-time Riccati equation solver.
Contents
Syntax
[Z, info] = ml_care_nwt_fac(A, B, C) [Z, info] = ml_care_nwt_fac(A, B, C, []) [Z, info] = ml_care_nwt_fac(A, B, C, [], opts)
[Z, info] = ml_care_nwt_fac(A, B, C, E) [Z, info] = ml_care_nwt_fac(A, B, C, E, opts)
Description
Computes the full-rank solutions of the standard algebraic Riccati equation
A'X + XA - XBB'X + C'C = 0, (1)
or of the generalized Riccati equation
A'XE + E'XA - E'XBB'XE + C'C = 0, (2)
with X = Z'*Z, using the Newton-Kleinman iteration. It is assumed that the eigenvalues of A (or s*E - A) lie in the open left half-plane, otherwise a stabilizing initial feedback K0 is given as parameter.
Input
A - matrix with dimensions n x n in (1) or (2) B - matrix with dimensions n x m in (1) or (2) C - matrix with dimensions p x n in (1) or (2) E - matrix with dimensions n x n in (2), if empty the standard equation (1) is solved opts - structure, containing the following optional entries:
Parameter | Meaning |
AbsTol | nonnegative scalar, tolerance for the absolute error in the last iteration step default: 0 |
Info | {0, 1}, used to disable/enable display of verbose status information during iteration steps default: 0 |
K0 | matrix with dimensions m x n, used to stabilize the spectrum of s*E - A, such that s*E - (A - BK0) has only stable eigenvalues |
lyapopts | structure, containing the optional parameters for Lyapunov equation solver, see ml_lyap_sgn_fac default: struct() |
MaxIter | positive integer, maximum number of iteration steps default: 100 |
RelTol | nonnegative scalar, tolerance for the relative error in the last iteration step default: 1.0e+02*n*eps |
Output
Z - full-rank solution factor of (1) or (2), such that X = Z'*Z info - structure, containing the following information:
Entry | Meaning |
AbsErr | vector, containing the absolute error of the solution matrix in each iteration step |
infoLYAP | array of structs, containing information about the used Lyapunov equations solver for every iteration step, see ml_lyap_sgn_fac |
IterationSteps | number of performed iteration steps |
RelErr | vector, containing the relative error of the solution matrix in each iteration step |
Reference
P. Benner, J. Saak, Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey, GAMM Mitteilungen 36 (1) (2013) 32--52. https://doi.org/10.1002/gamm.201310003
See Also