A software package for the solution of generalized algebraic Riccati equations. The generalized eigenvalue problem provides a powerful framework for the solution of quite general forms of algebraic Riccati equations arising in both continuous-and discrete-time applications. This general form is derived from control and filtering problems for systems in generalized (or implicit or descriptor) state space form. A software package called RICPACK has been developed to solve such Riccati equations by means of deflating subspaces for certain associated Hamiltonian or symplectic generalized eigenvalue problems. Utilizing an embedding technique, the package also calculates a solution even in cases where all cost or covariance matrices are singular or ill-conditioned with respect to inversion. Cross-weighting or correlated noise is handled directly. Both system-theoretic balancing and Ward’s balancing for the generalized eigenvalue problem are available to improve condition and accuracy. Condition estimates for the solution are also calculated. An iterative improvement calculation via Sylvester equations is available and can be used to generate new solutions for ”small” changes in the model. An interactive driver with numerous convenient default options has also been written. A numerical example is shown.

References in zbMATH (referenced in 46 articles )

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  1. Bouhamidi, A.; Hached, M.; Jbilou, K.: A preconditioned block Arnoldi method for large scale Lyapunov and algebraic Riccati equations (2016)
  2. Peretz, Yossi (Joseph): A randomized approximation algorithm for the minimal-norm static-output-feedback problem (2016)
  3. Frazho, A.E.; ter Horst, S.; Kaashoek, M.A.: State space formulas for a suboptimal rational Leech problem. I: Maximum entropy solution (2014)
  4. Bouhamidi, Abderrahman; Jbilou, Khalide: On the convergence of inexact Newton methods for discrete-time algebraic Riccati equations (2013)
  5. Bini, Dario A.; Iannazzo, Bruno; Meini, Beatrice: Numerical solution of algebraic Riccati equations. (2012)
  6. Benner, Peter; Faßbender, Heike: On the numerical solution of large-scale sparse discrete-time Riccati equations (2011)
  7. Bouhamidi, A.; Heyouni, M.; Jbilou, K.: Block Arnoldi-based methods for large scale discrete-time algebraic Riccati equations (2011)
  8. Tan, Jiajia; Zhang, JianQiu: An optimal adaptive filtering algorithm with a polynomial prediction model (2011)
  9. Gusev, Sergei; Johansson, Stefan; Kågström, Bo; Shiriaev, Anton; Varga, Andras: A numerical evaluation of solvers for the periodic Riccati differential equation (2010)
  10. Ignaciuk, Przemysław; Bartoszewicz, Andrzej: Linear-quadratic optimal control strategy for periodic-review inventory systems (2010)
  11. Ming, Zhang; Hong, Nie; Rupeng, Zhu: Stochastic optimal control of flexible aircraft taxiing at constant or variable velocity (2010)
  12. Rojas, Alejandro J.: Closed-form solution for a class of continuous-time algebraic Riccati equations (2010)
  13. Bauchau, Olivier A.; Wang, Jielong: Stability evaluation and system identification of flexible multibody systems (2007)
  14. Chu, Delin; Liu, Xinmin; Mehrmann, Volker: A numerical method for computing the Hamiltonian Schur form (2007)
  15. Ferrante, Augusto; Ntogramatzidis, Lorenzo: A unified approach to finite-horizon generalized LQ optimal control problems for discrete-time systems (2007)
  16. Benner, Peter; Byers, Ralph: An arithmetic for matrix pencils: theory and new algorithms (2006)
  17. Jbilou, K.: An Arnoldi based algorithm for large algebraic Riccati equations (2006)
  18. Li, Lei M.: Factorization of moving-average spectral densities by state-space representations and stacking (2005)
  19. Polyakov, K.Yu.: Singular $\cal H_2$-optimization problems for discrete-time systems (2005)
  20. Chu, M.; Del Buono, N.; Diele, F.; Politi, T.; Ragni, S.: On the semigroup of standard symplectic matrices and its applications (2004)

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