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.

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  1. Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens: A numerical comparison of different solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems (2020)
  2. Jbilou, Khalide; Raydan, Marcos: Nonlinear least-squares approach for large-scale algebraic Riccati equations (2019)
  3. Ovchinnikov, M. Yu.; Tkachev, S. S.; Shestopyorov, A. I.: Algorithms of stabilization of a spacecraft with flexible elements (2019)
  4. Yang, Yaguang: An efficient LQR design for discrete-time linear periodic system based on a novel lifting method (2018)
  5. Glover, Keith; Packard, Andrew: Some numerical considerations in (\mathcalH_\infty) control (2017)
  6. Kalabić, Uroš V.; Gupta, Rohit; Di Cairano, Stefano; Bloch, Anthony M.; Kolmanovsky, Ilya V.: MPC on manifolds with an application to the control of spacecraft attitude on SO(3) (2017)
  7. Bouhamidi, A.; Hached, M.; Jbilou, K.: A preconditioned block Arnoldi method for large scale Lyapunov and algebraic Riccati equations (2016)
  8. Mallia-Parfitt, Noeleene; Bröcker, Jochen: Assessing the performance of data assimilation algorithms which employ linear error feedback (2016)
  9. Ni, Boyi; Zhang, Qinghua: Stability of the Kalman filter for continuous time output error systems (2016)
  10. Peretz, Yossi (Joseph): A randomized approximation algorithm for the minimal-norm static-output-feedback problem (2016)
  11. Bänsch, Eberhard; Benner, Peter; Saak, Jens; Weichelt, Heiko K.: Riccati-based boundary feedback stabilization of incompressible Navier-Stokes flows (2015)
  12. Frazho, A. E.; ter Horst, S.; Kaashoek, M. A.: State space formulas for a suboptimal rational Leech problem. I: Maximum entropy solution (2014)
  13. Zerrik, El Hassan; Benslimane, Yassine; El Jai, Abdelhak: Regional gradient stabilization for bilinear distributed systems (2014)
  14. Bouhamidi, Abderrahman; Jbilou, Khalide: On the convergence of inexact Newton methods for discrete-time algebraic Riccati equations (2013)
  15. Maidi, Ahmed; Corriou, J. P.: Open-loop optimal controller design using variational iteration method (2013)
  16. Bini, Dario A.; Iannazzo, Bruno; Meini, Beatrice: Numerical solution of algebraic Riccati equations. (2012)
  17. Benner, Peter; Faßbender, Heike: On the numerical solution of large-scale sparse discrete-time Riccati equations (2011)
  18. Bouhamidi, A.; Heyouni, M.; Jbilou, K.: Block Arnoldi-based methods for large scale discrete-time algebraic Riccati equations (2011)
  19. Tan, Jiajia; Zhang, JianQiu: An optimal adaptive filtering algorithm with a polynomial prediction model (2011) ioport
  20. Gusev, Sergei; Johansson, Stefan; Kågström, Bo; Shiriaev, Anton; Varga, Andras: A numerical evaluation of solvers for the periodic Riccati differential equation (2010)

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