Solving the matrix differential riccati equation: A lyapunov equation approach

IEEE Transactions on Automatic Control

Volumn 55, Issue 1, 2010, Pages 191-194

  Nguyen, Thang ^a   Gajic, Zoran ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Algebraic Riccati equation; Differential Lyapunov equation; Differential Riccati equation; Optimal control

Indexed keywords

ALGEBRAIC RICCATI EQUATIONS; DIFFERENTIAL RICCATI EQUATION; LINEAR QUADRATIC OPTIMAL CONTROL PROBLEM; LYAPUNOV EQUATION; MATRIX; NUMERICAL EXAMPLE; OPTIMAL CONTROLS; TECHNICAL NOTES;

ALGEBRA; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; OPTIMIZATION; RICCATI EQUATIONS;

MATRIX ALGEBRA;

EID: 75549089157     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2033841     Document Type: Article

References (21)

1. R. E. Kalman, "Contribution to the theory of optimal control," Bol. Soc. Mat. Mex., vol.5, pp. 102-119, 1960.
2. C. Kenney and R. Leipnik, "Numerical integration of the differential matrix Riccati equation," IEEE Trans. Autom. Control, vol.AC-30, no.10, pp. 962-970, Oct. 1985.
3. E. J. Davison and M. C. Maki, "The numerical solution of the matrix Riccati differential equation," IEEE Trans. Autom. Control, vol.AC-18, no.1, pp. 71-73, Feb. 1973.
4. B. D. O. Anderson and J. B. Moore, Linear Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1971.
5. J. E. Prussing, "The numerical solution of the matrix Riccati differential equation," Int. J. Control, vol.15, pp. 995-1000, 1972.
6. R. B. Leipnik, "A canonical form and solution for the matrix Riccati differential equation," J. Austral. Math. Soc. Ser. B, vol.26, pp. 355-361, 1985.
7. J. Nazarzadeh, M. Razzaghi, and K. Y. Nikravesh, "Solution of the matrix Riccati equation for the linear quadratic control problems," Mathl. Comput. Modelling, vol.27, pp. 51-55, 1998.
8. L. Vandenberghe, V. Balakrishnan, R. Wallin, A. Hansson, and T. Roh, "Interior-point methods for semidefinite programming problems derived from the KYP lemma," in Positive Polynomials in Control, D. Henrion and A. Garulli, Eds. Berlin, Germany: Springer Verlag, 2005, vol.312/2005, pp. 195-238.
9. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems. New York: Wiley, 1972.
10. D. L. Kleinman, "On the iterative technique for Riccati equation computations," IEEE Trans. Autom. Control, vol.AC-13, no.1, pp. 114-115, Feb. 1968.
11. V. Kecman, S. Bingulac, and Z. Gajic, "Eigenvector approach for order-reduction of singularly perturbed linear-quadratic optimal control problems," Automatica, vol.35, pp. 151-158, 1999.
12. R. Byers, "Solving the algebraic Riccati equation with the matrix sign function," Lin. Alg. Appl., vol.85, pp. 267-279, 1987.
13. J. E. Potter, "Matrix quadratic solutions," J. SIAM Appl. Math., vol.14, pp. 496-501, 1966.
14. A. J. Laub, "A Schur method for solving algebraic Riccati equations," IEEE Trans. Autom. Control, vol.AC-24, no.6, pp. 913-921, Dec. 1979.
15. V. Sima, Algorithms for Linear-Quadratic Optimization. New York: Marcel Dekker Inc, 1996.
16. W. A. Coppel, "Matrix quadratic equations," Bull. Austral. Math. Soc., vol.10, pp. 377-401, 1974.
17. 2+ D,X(0)= C," IEEE Trans. Autom. Control, vol.AC-25, no.6, pp. 1138-1141, Dec. 1980.
18. Z. Gajic and M. Qureshi, The Lyapunov Matrix Equation in System Stability and Control. New York: Dover Publications, 2008.
19. S. Hammarling, "Numerical solution of the stable, non-negative definite Lyapunov equation," IMA J. Num. Anal., vol.2, pp. 303-325, 1982.
20. N. J. Higham, "The scaling and squaring method for the matrix exponential revisited," SIAM J. Matrix Anal. Appl., vol.26, pp. 1179-1193, 2005.
21. Y. Arkun and S. Ramakrishnan, "Bounds on the optimum quadratic cost of structure-constrained controllers," IEEE Trans. Autom. Control, vol.AC-28, no.9, pp. 924-927, Sep. 1983.