{"id":"W2104744926","doi":"10.1002/nla.622","title":"Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems","year":2008,"lang":"en","type":"article","venue":"Numerical Linear Algebra with Applications","topic":"Model Reduction and Neural Networks","field":"Physics and Astronomy","cited_by":344,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"","keywords":"Algebraic Riccati equation; Mathematics; Cholesky decomposition; Linear-quadratic regulator; Riccati equation; Lyapunov equation; Linear-quadratic-Gaussian control; Linear system; Applied mathematics; Lyapunov function; Optimal control; Mathematical optimization; Differential equation; Mathematical analysis; Nonlinear system","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001287262,0.0002468043,0.0003791799,0.00008675022,0.0004776341,0.00001892463,0.0001651392,0.00008148538,0.0002201135],"category_scores_gemma":[0.00001631022,0.0002108702,0.0001010918,0.0006533238,0.0002069405,0.00018483,0.00003580463,0.0002999956,0.00006986359],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002352302,"about_ca_system_score_gemma":0.0001222168,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008205155,"about_ca_topic_score_gemma":0.000001436037,"domain_scores_codex":[0.9982565,0.00008741492,0.0005498402,0.0004498666,0.0002979879,0.0003583776],"domain_scores_gemma":[0.9986252,0.0002474151,0.0002897008,0.0003814654,0.000223184,0.0002329893],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0006199517,0.009695048,0.07125976,0.0002788591,0.001080051,0.000004237592,0.003812341,0.5084563,0.003976566,0.3356605,0.003612388,0.06154397],"study_design_scores_gemma":[0.001410291,0.0001871563,0.001110132,0.00002167028,0.0001059147,0.000008141072,0.0001310801,0.9899899,0.0004135699,0.0008899947,0.005387137,0.000345006],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01132833,0.000178269,0.9858865,0.0009566158,0.00002904279,0.0009770945,0.00007594128,0.00008783016,0.0004803584],"genre_scores_gemma":[0.9670925,0.0000210649,0.03111456,0.0001274456,0.00033724,0.000779829,0.000249752,0.00003566723,0.0002419432],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9557642,"threshold_uncertainty_score":0.8599039,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0146462960125644,"score_gpt":0.2505833551941164,"score_spread":0.235937059181552,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}