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Verification of algebraic Riccati equations

These files contain methods to compute a verified enclosure of the stabilizing solution of an algebraic Riccati equation.

To run the methods, you will need to install:

All these packages need to be installed in a folder which is to be included in the Matlab path. For instance, initialize with

addpath('path_to_pgdoubling')
addpath('path_to_xunit/xunit')
addpath('path_to_carex')
addpath('path_to_Miyajima_CARE')
startintlab

and then re-run our experiments with

experiments_all_ChuLMcarex({@verifycare,@verifycare_hat_permuted_replace,@Mn_wrapper,@verifycare_fixedpoint_permuted})
experiments_scaled_carex(15, {@verifycare,@verifycare_hat_permuted_replace,@Mn_wrapper,@verifycare_fixedpoint_permuted})

You can configure the method used to solve CAREs in floating-point arithmetic by editing care_solution.m, for instance, to use solveCARE_Miyajima instead of solveCARE_schur.

Authors

  • Tayyebe Haqiri (S. Bahonar University, Kerman, Iran), thaqiri at gmail.com
  • Federico Poloni (University of Pisa, Italy), federico.poloni at unipi.it