An efficient algorithm - GRICSR - for solving continuous-time algebraic matrix Riccati equations (CAREs) is presented and numerical results obtained by using its implementation are dis cussed. The gorithm employs condition-controlled Gaussian symplectic transformations, a sym metric updating scheme for computing the stabilizing solution of CARE, and accurate approx imations of the eigenvalues of the Hamiltonian matrix involved in the optimal control problem; these eigenvalues are used as shifts in an QR-like process. The Hamiltonian structure is preserved throughout the algorithm. The main computational steps are sketched, and details of the Fortran implementation are mentioned. Numerical results show that the algorithm can be used safely, even when large values of condition numbers of the transformation matrices are allowed.
Computational methods; control system design; eigenvalues; Hamiltonian matrices; invariant subspaces; linear algebra; optimal control; symplectic matrices.
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