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Volumn 17, Issue 5, 1997, Pages 18-28

Benchmarks for the Numerical Solution of Algebraic Riccati Equations

Author keywords

[No Author keywords available]

Indexed keywords

CONTROLLABILITY; DATA REDUCTION; NUMERICAL ANALYSIS; OPTIMIZATION; RICCATI EQUATIONS; SET THEORY;

EID: 0031249047     PISSN: 1066033X     EISSN: None     Source Type: Journal    
DOI: 10.1109/37.621466     Document Type: Article
Times cited : (40)

References (59)
  • 1
    • 0014738902 scopus 로고
    • On the State Estimation in Switching Environments
    • G. Ackerson and K. Fu, “On the State Estimation in Switching Environments,” IEEE Trans Automat Control, AC-15 10-17, 1970
    • (1970) IEEE Trans Automat Control , vol.AC-15 , pp. 10-17
    • Ackerson, G.1    Fu, K.2
  • 2
    • 0001874303 scopus 로고
    • A Multxhift Algorithm for the Numerical Solution of Algebraic Riccati Equations
    • G. S. Ammar, P. Benner, and V. Mehrmann, “A Multxhift Algorithm for the Numerical Solution of Algebraic Riccati Equations,” Electr Trans Num Anal, 1 33-48, 1993
    • (1993) Electr Trans Num Anal , vol.1 , pp. 33-48
    • Ammar, G.S.1    Benner, P.2    Mehrmann, V.3
  • 4
    • 85008004718 scopus 로고
    • On the Numerical Solution of Algebraic Matrix kccati Equations
    • Ph D thesis, Univ of Southem California, Dept of Elec Eng-Systems, Los Angeles, CA, December
    • W. F. Amold, “On the Numerical Solution of Algebraic Matrix kccati Equations,” Ph D thesis, Univ of Southem California, Dept of Elec Eng-Systems, Los Angeles, CA, December 1983 26
    • (1983) , vol.26
    • Amold, W.F.1
  • 5
    • 0021618667 scopus 로고
    • Generalized Eigenproblem Algorithms and Software for Algebraic Riccati Equations
    • W.F. Amold 111 and A.J. Laub, “Generalized Eigenproblem Algorithms and Software for Algebraic Riccati Equations,” Proc. IEEE, 72:1746-1754, 1984.
    • (1984) Proc. IEEE , vol.72 , pp. 1746-1754
    • Amold, W.F.1    Laub, A.J.2
  • 6
    • 0014164440 scopus 로고
    • A System for the Optimal and Suboptimal Position and Velocity Control for a String of High-speed Vehicles
    • Lausanne, Switzer-land, September
    • M.Athans, W.S. Levine, and A. Levis, “A System for the Optimal and Suboptimal Position and Velocity Control for a String of High-speed Vehicles,” in Proc. 5th Int. Analogue Computation Meetings, Lausanne, Switzer-land, September 1967.
    • (1967) Proc. 5th Int. Analogue Computation Meetings
    • Athans, M.1    Levine, W.S.2    Levis, A.3
  • 7
    • 0008256783 scopus 로고
    • Inverse Free Parallel Method for the Numerical Solution of Algebraic Riccati Equations
    • in J.G. Lewis, editor, Snowbird, UT, Philadelphia, PA, SIAM.
    • Z.Bai and Q.Qian, “Inverse Free Parallel Method for the Numerical Solution of Algebraic Riccati Equations,” in J.G. Lewis, editor, Proc. Fifth SIAM Conf. Appl. Lin. Alg., Snowbird, UT, pp. 167-171, Philadelphia, PA, 1994. SIAM.
    • (1994) Proc. Fifth SIAM Conf. Appl. Lin. Alg. , pp. 167-171
    • Bai, Z.1    Qian, Q.2
  • 8
    • 0024704840 scopus 로고
    • Robust Control System Design with a Proportional-Integral Observer
    • S.Beale and B.Shafai, “Robust Control System Design with a Proportional-Integral Observer,” Internat. J. Control, 50:97-111, 1989.
    • (1989) Internat. J. Control , vol.50 , pp. 97-111
    • Beale, S.1    Shafai, B.2
  • 9
    • 5244373881 scopus 로고
    • Step Size Control for Newton's Method Applied to Algebraic Riccati Equations
    • in J.G. Lewis, editor, Snowbird, UT, Philadelphia, PA, SIAM.
    • P. Benner and R. Byers, “Step Size Control for Newton's Method Applied to Algebraic Riccati Equations,” in J.G. Lewis, editor, Proc. Fifth SIAM Conf. AppZ. Lin. Alg., Snowbird, UT, pp. 177-181, Philadelphia, PA, 1994. SIAM.
    • (1994) Proc. Fifth SIAM Conf. AppZ. Lin. Alg. , pp. 177-181
    • Benner, P.1    Byers, R.2
  • 10
    • 84889559762 scopus 로고    scopus 로고
    • An Exact Line Search Method for Solving Generalized Continuous-Time Algebraic Riccati Equations
    • To appear.
    • P. Benner andR. Byers, “An Exact Line Search Method for Solving Generalized Continuous-Time Algebraic Riccati Equations,” IEEE Trans. Automat. Control, 1997. To appear.
    • (1997) IEEE Trans. Automat. Control
    • Benner, P.1    Byers, R.2
  • 11
    • 0003418313 scopus 로고    scopus 로고
    • A Collection of Benchmark Examples for the Numerical Solution of Algebraic Riccati Equations I: Continuous-Time Case
    • Fak. f. Mathematik, TU Chemnitz-Zwickau, 09107 Chemnitz, FRG, 1995. Available from http://www.tu-chemnitz.de/sfb393/spc95pr.html.
    • P.Benner, A.Laub, and V.Mehrmann, “A Collection of Benchmark Examples for the Numerical Solution of Algebraic Riccati Equations I: Continuous-Time Case,” Technical Report SPC 9522, Fak. f. Mathematik, TU Chemnitz-Zwickau, 09107 Chemnitz, FRG, 1995. Available from http://www.tu-chemnitz.de/sfb393/spc95pr.html.
    • Technical Report SPC 9522
    • Benner, P.1    Laub, A.2    Mehrmann, V.3
  • 12
    • 0003418313 scopus 로고    scopus 로고
    • A Collection of Benchmark Examples for the Numerical Solution of Algebraic Riccati Equations 11: Discrete-Time Case
    • Fak. f. Mathematik, TU Chemnitz-Zwickau, 09107 Chemnitz, FRG, 1995. Available from http://www.tu-chemnitz.de/sfb393/spc95pr.html.
    • P. Benner, A. Laub, and V.Mehrmann, “A Collection of Benchmark Examples for the Numerical Solution of Algebraic Riccati Equations 11: Discrete-Time Case.” Technical Report SPC 9523, Fak. f. Mathematik, TU Chemnitz-Zwickau, 09107 Chemnitz, FRG, 1995. Available from http://www.tu-chemnitz.de/sfb393/spc95pr.html.
    • Technical Report SPC 9523
    • Benner, P.1    Laub, A.2    Mehrmann, V.3
  • 14
    • 0018109751 scopus 로고
    • Application of Steady-State Kalman Filters-Theory with Field Results
    • Philadelphia, PA
    • W.L. Bialkowski, “Application of Steady-State Kalman Filters-Theory with Field Results,” in Proc. Joint Automat. Cont. Conf., Philadelphia, PA, 1978.
    • (1978) Proc. Joint Automat. Cont. Conf.
    • Bialkowski, W.L.1
  • 17
    • 0011016021 scopus 로고
    • Numerical Condition of the Algebraic Riccati Equation
    • R. Byers, “Numerical Condition of the Algebraic Riccati Equation,” Contemp. Math., 47:35-49, 1985.
    • (1985) Contemp. Math. , vol.47 , pp. 35-49
    • Byers, R.1
  • 18
    • 38249038136 scopus 로고
    • Solving the Algebraic Riccati Equation with the Matrix Sign Function
    • R. Byers, “Solving the Algebraic Riccati Equation with the Matrix Sign Function,” Linear Algebra Appl., 85:267-279, 1987.
    • (1987) Linear Algebra Appl. , vol.85 , pp. 267-279
    • Byers, R.1
  • 19
    • 0017012825 scopus 로고
    • A Decomposition of Near-Optimum Regulators for Systems with Slow and Fast Modes
    • J. Chow and P. Kokotovic, “A Decomposition of Near-Optimum Regulators for Systems with Slow and Fast Modes,” IEEE Trans. Automat. Control, AC-21:701-705, 1976
    • (1976) IEEE Trans. Automat. Control , vol.AC-21 , pp. 701-705
    • Chow, J.1    Kokotovic, P.2
  • 20
    • 0040503538 scopus 로고
    • The Systematic Design of Control Systems for the Multivariable Servomechanism Problem
    • in M.K Sain, J.L. Peczltowsky, and J.M. Melsa, editors, Chicago, IL
    • E.J. Davison and W. Gesing, “The Systematic Design of Control Systems for the Multivariable Servomechanism Problem,” in M.K Sain, J.L. Peczltowsky, and J.M. Melsa, editors, Alternatives for Linear Multivariable Control, Nat. Eng. Consortium Inc., Chicago, IL, 1978.
    • (1978) Alternatives for Linear Multivariable Control, Nat. Eng. Consortium Inc.
    • Davison, E.J.1    Gesing, W.2
  • 23
    • 0022788010 scopus 로고
    • A Generalization of the Matrix-Sign-Function Solution for Algebraic Riccati Equations
    • (See also Proc. 1985 CDC, pp. 1233-1235.)
    • J.D. Gardiner and A.J. Laub, “A Generalization of the Matrix-Sign-Function Solution for Algebraic Riccati Equations,” Iriternat. J. Control, 44:823-832, 1986. (See also Proc. 1985 CDC, pp. 1233-1235.)
    • (1986) Iriternat. J. Control , vol.44 , pp. 823-832
    • Gardiner, J.D.1    Laub, A.J.2
  • 24
    • 0019031813 scopus 로고
    • A Suboptimal Controller for Minimum Sensitivity of Closed-Loop Eigenvalues to Parameter Variations
    • E. Gomathi, S. Prabhu, and M. Pai, “A Suboptimal Controller for Minimum Sensitivity of Closed-Loop Eigenvalues to Parameter Variations,” IEEE Trans. Automat. Control, AC-25:587-588, 1980.
    • (1980) IEEE Trans. Automat. Control , vol.AC-25 , pp. 587-588
    • Gomathi, E.1    Prabhu, S.2    Pai, M.3
  • 25
    • 0026851353 scopus 로고
    • Scaling of the Discrete-Time Algebraic Riccati Equation to Enhance Stability of the Schur Solution Metbod
    • T. Gudmundsson, C. Kenney, and A.J. Laub, “Scaling of the Discrete-Time Algebraic Riccati Equation to Enhance Stability of the Schur Solution Metbod,” IEEE Trans. Automat, Control, 37513-518, 1992.
    • (1992) IEEE Trans. Automat, Control , pp. 37513-37518
    • Gudmundsson, T.1    Kenney, C.2    Laub, A.J.3
  • 27
    • 0015109409 scopus 로고
    • An Iterative Technique for the Computation of Steady State Gains for the Discrete Optimal Regulator
    • G.A. Hewer, “An Iterative Technique for the Computation of Steady State Gains for the Discrete Optimal Regulator,” IEEE Trans. Automat. Control, ACc-16:382-384, 1971.
    • (1971) IEEE Trans. Automat. Control , vol.ACc-16 , pp. 382-384
    • Hewer, G.A.1
  • 29
    • 0001122178 scopus 로고
    • On Computing the Stabilizing Solution of the Discrete-Time Riccati Equation
    • V. Ionescu and M. Weiss, “On Computing the Stabilizing Solution of the Discrete-Time Riccati Equation,” LineurAlgebra Appl., 174:229-238,1992.
    • (1992) LineurAlgebra Appl. , vol.174 , pp. 229-238
    • Ionescu, V.1    Weiss, M.2
  • 30
    • 0019579162 scopus 로고
    • On the Existence of a Negative Semidefinite Antistabilizing Solution to the Discrete Algebraic Riccati Equation
    • E.I. Jonckheere, “On the Existence of a Negative Semidefinite Antistabilizing Solution to the Discrete Algebraic Riccati Equation,” IEEE Trans. Autoniat. Control, AC-26:707-712, 1981.
    • (1981) IEEE Trans. Autoniat. Control , vol.AC-26 , pp. 707-712
    • Jonckheere, E.I.1
  • 31
    • 0025226853 scopus 로고
    • The Sensitivity of the Algebraic and Differential Riccati Equations
    • C. Kenney and G. Hewer, “The Sensitivity of the Algebraic and Differential Riccati Equations,” SIAM J. Cont. Optim., 28:50-69, 1990.
    • (1990) SIAM J. Cont. Optim. , vol.28 , pp. 50-69
    • Kenney, C.1    Hewer, G.2
  • 32
    • 0024641418 scopus 로고
    • A Stability-Enhancing Scaling Procedure for Schur-Riccati Solvers
    • C. Kenney, A.J. Laub, and M. Wette, “A Stability-Enhancing Scaling Procedure for Schur-Riccati Solvers,” Sys. Control Lett., 12:241-250,1989.
    • (1989) Sys. Control Lett. , vol.12 , pp. 241-250
    • Kenney, C.1    Laub, A.J.2    Wette, M.3
  • 33
    • 84914965022 scopus 로고
    • On an Iterative Technique for Riccati Equation Computations
    • D.L. Kleinman, “On an Iterative Technique for Riccati Equation Computations,” IEEE Trans. Automat. Control, AC-13:114-115, 1968.
    • (1968) IEEE Trans. Automat. Control , vol.AC-13 , pp. 114-115
    • Kleinman, D.L.1
  • 34
    • 0013136925 scopus 로고
    • Perturbation Analysis of the Discrete Riccati Equation
    • P.M. Konstantinov, P. H. R. Petkov, and N.D. Christov, “Perturbation Analysis of the Discrete Riccati Equation,” Kybernetica, 29: 18-29, 1993.
    • (1993) Kybernetica , vol.29 , pp. 18-29
    • Konstantinov, P.M.1    Petkov, P.H.R.2    Christov, N.D.3
  • 36
    • 0004074291 scopus 로고
    • The Algebraic Riccati Equation
    • P: Lancaster and L. Rodman, Oxford University Press, Oxford
    • P: Lancaster and L. Rodman, The Algebraic Riccati Equation, Oxford University Press, Oxford, 1995.
    • (1995)
  • 38
    • 0018681625 scopus 로고
    • A Schur Method for Solving Algebraic Riccati Equations
    • (See also Proc. 1978 CDC I Jan. 19791, pp. 60-65.)
    • A.J. Lauh, “A Schur Method for Solving Algebraic Riccati Equations,” IEEE Trans. Automat. Control, AC-24:913-921, 1979. (See also Proc. 1978 CDC I Jan. 19791, pp. 60-65.)
    • (1979) IEEE Trans. Automat. Control , vol.AC-24 , pp. 913-921
    • Lauh, A.J.1
  • 39
    • 0002756084 scopus 로고
    • Invariant Subspace Methods for the Numerical Solution of Riccati Equations
    • in S. Bittanti, A.J. Laub, and J.C. Willems, editors, The Riccari Equation, Springer-Verlag, Berlin
    • A.J. Lauh, “Invariant Subspace Methods for the Numerical Solution of Riccati Equations,” in S. Bittanti, A.J. Laub, and J.C. Willems, editors, The Riccari Equation, pp. 163-196. Springer-Verlag, Berlin, 1991.
    • (1991) , pp. 163-196
    • Lauh, A.J.1
  • 41
    • 4243564445 scopus 로고
    • Sampled-Data Control of Systems with Slow and Fast Modes
    • Ph.D. thesis, Michigan State University
    • B. Litkouhi, “Sampled-Data Control of Systems with Slow and Fast Modes,” Ph.D. thesis, Michigan State University, 1983.
    • (1983)
    • Litkouhi, B.1
  • 42
    • 38248998777 scopus 로고
    • An Iterative Algorithm for the Solution of the Discrete Time Algebraic Riccati Equation
    • L.Z. Lu and W.W. Lin, “An Iterative Algorithm for the Solution of the Discrete Time Algebraic Riccati Equation,” Linear Algebra Appl., 188/189: 465-488, 1993.
    • (1993) Linear Algebra Appl. , vol.188-189 , pp. 465-488
    • Lu, L.Z.1    Lin, W.W.2
  • 44
    • 21344456693 scopus 로고    scopus 로고
    • A Step Toward a Unified Treatment of Continuous and Discrete Time Control Problems
    • V. Mehrmann, “A Step Toward a Unified Treatment of Continuous and Discrete Time Control Problems,” Linear Algebra Appl., 241-243:749-779, 1996.
    • (1996) Linear Algebra Appl. , vol.241-243 , pp. 749-779
    • Mehrmann, V.1
  • 45
    • 0027844491 scopus 로고
    • On Scaling an Algebraic Riccati Equation
    • San Francisco, CA, June
    • P. Pandey, “On Scaling an Algebraic Riccati Equation,” in Proc. American Control Conf., pp. 1583-1587, San Francisco, CA, June 1993.
    • (1993) Proc. American Control Conf. , pp. 1583-1587
    • Pandey, P.1
  • 46
    • 0019045717 scopus 로고
    • On the Numerical Solution of the Discrete-Time Algebraic Riccati Equation
    • T. Pappas, A.J. Laub, and N.R. Sandell, “On the Numerical Solution of the Discrete-Time Algebraic Riccati Equation,” IEEE Truns. Automat. Control, AC-25:631-641, 1980.
    • (1980) IEEE Truns. Automat. Control , vol.AC-25 , pp. 631-641
    • Pappas, T.1    Laub, A.J.2    Sandell, N.R.3
  • 47
    • 0000292291 scopus 로고
    • Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors
    • B.N. Parlett and C.Reinsch, “Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors, Numer: Math., 13:296-304, 1969.
    • (1969) Numer: Math. , vol.13 , pp. 296-304
    • Parlett, B.N.1    Reinsch, C.2
  • 48
    • 0019049103 scopus 로고
    • Computer Control Algorithms for a Tubular Ammonia Reactor
    • L.M. Patnaik, N. Viswanadham, and I.G. Sarma, “Computer Control Algorithms for a Tubular Ammonia Reactor,” IEEE Trans. Automat. Control, AC-25(4):642-651, 1980.
    • (1980) IEEE Trans. Automat. Control , vol.AC-25 , Issue.4 , pp. 642-651
    • Patnaik, L.M.1    Viswanadham, N.2    Sarma, I.G.3
  • 51
    • 85008052438 scopus 로고
    • A Posteriori Error Analysis of the Generalized Schur Approach for Solving the Discrete Matrix Riccati Equation
    • preprint, Department of Automatics, 1756 Sofia, Bulgaria
    • P.H. Petkov, N.D. Christov, andM.M. Konstantinov, “A Posteriori Error Analysis of the Generalized Schur Approach for Solving the Discrete Matrix Riccati Equation,” preprint, Department of Automatics, Higher Institute of Mechanical and Electrical Engineering, 1756 Sofia, Bulgaria, 1989.
    • (1989) Higher Institute of Mechanical and Electrical Engineering
    • Petkov, P.H.1    Christov, N.D.2    Konstantinov, M.M.3
  • 52
    • 0023410389 scopus 로고
    • On the Numerical Properties of the Schur Approach for Solving the Matrix Riccati Equation
    • P.H. Petkov, N.D. Christov, and M.M. Konstantinov, “On the Numerical Properties of the Schur Approach for Solving the Matrix Riccati Equation,” Sys. Control Lett., 9:197-201, 1987.
    • (1987) Sys. Control Lett. , vol.9 , pp. 197-201
    • Petkov, P.H.1    Christov, N.D.2    Konstantinov, M.M.3
  • 53
    • 0019069037 scopus 로고
    • Linear Model Reduction and Solution of the Algebraic Riccati Equation by Use of the Sign Function
    • (reprint of Technical Report No. TR-13, CUEDB-Control, Cambridge University, Engineering Department, 1971).
    • J.D. Roberts, “Linear Model Reduction and Solution of the Algebraic Riccati Equation by Use of the Sign Function,” Internat. J. Control, 32:677-687, 1980 (reprint of Technical Report No. TR-13, CUEDB-Control, Cambridge University, Engineering Department, 1971).
    • (1980) Internat. J. Control , vol.32 , pp. 677-687
    • Roberts, J.D.1
  • 54
    • 0000010902 scopus 로고
    • A Multi-Level Technique for the Approximate Solution of Operator Lyapunov and Algebraic Riccati Equations
    • I.G. Rosen and C.Wang, “A Multi-Level Technique for the Approximate Solution of Operator Lyapunov and Algebraic Riccati Equations,” SIAM J. Numel: Anal., 32(2):514-541, 1995.
    • (1995) SIAM J. Numel: Anal. , vol.32 , Issue.2 , pp. 514-541
    • Rosen, I.G.1    Wang, C.2
  • 56
    • 0016940348 scopus 로고
    • Pole Assignment with Minimum Eigen-value Sensitivity to Parameter Variations
    • V.G. Shankar and K.Ramar, “Pole Assignment with Minimum Eigen-value Sensitivity to Parameter Variations,” Internat. J. Control, 23:493-504, 1976.
    • (1976) Internat. J. Control , vol.23 , pp. 493-504
    • Shankar, V.G.1    Ramar, K.2
  • 57
    • 0039579465 scopus 로고
    • Backward Error of the Discrete-Time Algebraic Riccati Equation
    • preprint, Dept. Computing Science, Umed University, Umeb, Sweden
    • J.Sun, “Backward Error of the Discrete-Time Algebraic Riccati Equation,” preprint, Dept. Computing Science, Umed University, Umeb, Sweden, 1995.
    • (1995)
    • Sun, J.1
  • 58
    • 0000669144 scopus 로고
    • A Generalized Eigenvalue Approach for Solving Riccati Equations
    • P. Van Dooren, “A Generalized Eigenvalue Approach for Solving Riccati Equations,” SIAM J. Sci. Statist. Comput., 2:121-135, 1981.
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 121-135
    • Van Dooren, P.1
  • 59
    • 0000059741 scopus 로고
    • A Symplectic Method for Approximating All the Eigen-values of a Hamiltonian Matrix
    • C.F. Van Loan, “A Symplectic Method for Approximating All the Eigen-values of a Hamiltonian Matrix,” Linear Algebra Appl., 16:233-251, 1984.
    • (1984) Linear Algebra Appl. , vol.16 , pp. 233-251
    • Van Loan, C.F.1


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