Approximation of solutions of riccati equations

SIAM Journal on Control and Optimization

Volumn 44, Issue 4, 2005, Pages 1419-1435

  Bubák, Pavel ^a   Van Der Mee, Cornelis V M ^b   Ran, André C M ^c  

^a Doktorand MUUK   (Czech Republic)

^b UNIVERSITY OF CAGLIARI   (Italy)

^c VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Exponential dichotomy; Matrix approximation; Riccati equation

Indexed keywords

APPROXIMATION THEORY; CONTROL SYSTEMS; INVARIANCE; MATHEMATICAL OPERATORS; OPTIMIZATION; PROBLEM SOLVING;

EXPONENTIAL DICHOTOMY; FINITE DIMENSIONAL APPROXIMANTS; INVARIANT SUBSPACE APPROACH; MATRIX APPROXIMATIONS;

RICCATI EQUATIONS;

EID: 33746034965     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012903436843     Document Type: Article

References (20)

1. T. YA. AZIZOV AND I. S. IOKHVIDOV, Linear Operators in Spaces with an Indefinite Metric, John Wiley, Chichester, 1989.
2. H. T. BANKS AND K. KUNISCH, The linear regulator problem for parabolic systems, SIAM J. Control Optim., 22 (1984), pp. 684-698.
3. H. BART, I. GOHBERG, AND M. A. KAASHOEK, Minimal Factorization of Matrix and Operator Functions, Birkhäuser, Basel, 1979.
4. H. BART, I. GOHBERG, AND M. A. KAASHOEK, Wiener-Hopf factorization, inverse Fourier transforms and exponentially dichotomous operators, J. Funct. Anal., 68 (1986), pp. 1-42.
5. H. BART, I. GOHBERG, AND M. A. KAASHOEK, Wiener-Hopf equations with symbols analytic in a strip, Constructive Methods of Wiener-Hopf Factorization Oper. Theory Adv. Appl., I. Gohberg and M. A. Kaashoek, eds., Birkhäuser, Basel, Switzerland, 1986, pp. 39-74.
6. S. BOCHNER AND R. S. PHILLIPS, Absolutely convergent Fourier expansions for non-commutative normed rings, Ann. of Math., 43 (1942), pp. 409-418.
7. R. F. CURTAIN AND H. ZWART, An Introduction to Infinite-Dimensional Linear Systems Theory, Springer, New York, 1995.
8. J. S. GIBSON, Linear-quadratic optimal control of hereditary differential systems: Infinite dimensional Riccati equations and numerical approximations, SIAM J. Control Optim., 21 (1983), pp. 95-139.
9. I. C. GOHBERG AND J. LEITERER, The factorization of operator functions with respect to a contour. II. The canonical factorization of operator functions close to the identity, Math. Nach., 54 (1972), pp. 41-74 (in Russian). Appendix.
10. W. GREENBERG, V. PROTOPOPESCU, AND C. V. M. VAN DER MEE, Boundary Value Problems in Abstract Kinetic Theory, Birkhäuser, Verlag, Basel, Switzerland, 1987.
11. J. K. HALE AND S. M. VERDUYN-LUNEL, Introduction to Functional Differential Equations, Applied Mathematical Sciences 99, Springer, New York, 1993.
12. K. ITO, Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hubert spaces, Distributed Parameter Systems, F. Kappel, K. Kunisch, and W. Schappacher, eds., Springer, New York, 1987, pp. 151-166.
13. K. ITO, Finite-dimensional compensators for infinite-dimensional systems via Galerkin-type approximation, SIAM J. Control Optim., 28 (1990), pp. 1251-1269.
14. ∞ control, SIAM J. Control Optim., 36 (1998), pp. 82-99.
15. ∞ -Control for Distributed Parameter Systems: A State-space Approach, Birkhäuser, Boston, 1993.
16. C. R. KUIPER AND H. J. ZWART, Connections between the algebraic Riccati equation and the Hamiltonian for Riesz-spectral systems, J. Math. Systems, Estim. Control, 6 (1996), pp. 1-48.
17. P. LANCASTER AND L. RODMAN, Algebraic Riccati Equations, Oxford University Press, New York, 1995.
18. H. LANGER, A. C. M. RAN, AND B. A. VAN DE ROTTEN, Invariant subspaces of infinite dimensional Hamiltonians and solutions of the corresponding Riccati equations, Linear Operators and Matrices, Oper. Theory Adv. Appl., I. Gohberg and H. Langer, eds., Birkhäuser, Basel and Boston, 2002, pp. 235-254.
19. C. V. M. VAN DER MEE AND A. C. M. RAN, Perturbation results for exponentially dichotomous operators on general Banach spaces, J. Funct. Anal., 210 (2004), pp. 193-213.
20. J. C. OOSTVEEN, R. F. CURTAIN, AND K. ITO, An approximation theory for strongly stabilizing solutions to the operator LQ Riccati equation, SIAM J. Control Optim., 38 (2000), pp. 1909-1937.