ml_pcare_nwt_fac
Positive continuous-time Riccati equation solver.
Contents
Syntax
[Z, info] = ml_pcare_nwt_fac(A, B, C) [Z, info] = ml_pcare_nwt_fac(A, B, C, []) [Z, info] = ml_pcare_nwt_fac(A, B, C, [], opts)
[Z, info] = ml_pcare_nwt_fac(A, B, C, E) [Z, info] = ml_pcare_nwt_fac(A, B, C, E, opts)
Description
Computes the full-rank solutions of the standard positive Riccati equation
A'*X + X*A + X*B*B'*X + C'*C = 0, (1)
or of the generalized positive Riccati equation
A'*X*E + E'*X*A + E'*X*B*B'*X*E + C'*C = 0, (2)
with X = Z*Z', using the low-rank Newton iteration. It is assumed that the eigenvalues of A (or s*E - A) lie in the open left half-plane and that the equation (1) (or (2)) has a solution.
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 |
CompTol | nonnegative scalar, tolerance for the row compression during the iteration default: 1.0e-02*sqrt(n*eps) |
Info | {0, 1}, used to disable/enable display of verbose status information during iteration steps default: 0 |
lyapopts | structure, containing the optional parameters for the Lyapunov equation solver used in every iteration step, 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 - low-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
A. Varga, On computing high accuracy solutions of a class of Riccati equations, Control-Theory and Advanced Technology 10 (4) (1995) 2005--2016.
See Also