Classical solutions of nonautonomous Riccati equations arising in parabolic boundary control problems, II

Applied Mathematics and Optimization

Volumn 41, Issue 2, 2000, Pages 199-226

  Acquistapace, P ^a   Terreni, B ^b  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF MILAN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; CONTROLLABILITY; MATHEMATICAL OPERATORS; OPTIMAL CONTROL SYSTEMS; RICCATI EQUATIONS;

NONAUTONOMOUS RICCATI EQUATIONS; PARABOLIC BOUNDARY CONTROL;

LINEAR CONTROL SYSTEMS;

EID: 0034148951     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459911011     Document Type: Article

References (30)

1. Acquistapace P (1988), Evolution operators and strong solutions of abstract linear parabolic equations, Diff Int Eq 1:433-457
2. Acquistapace P (1991), On a family of generators of analytic semigroups, in Semigroup Theory and Evolution Equations, (proceedings, Delft, 1989) (Clément Ph, Mitidieri E, de Pagter B, editors). Lecture Notes in Pure and Applied Mathematics 135, Marcel Dekker, New York, pp 1-14
3. Acquistapace P (1994), Boundary control for non-autonomous parabolic equations in non-cylindrical domains, in Boundary Control and Variation (proceedings, Sophia-Antipolis, 1992) (Zolésio JP, editor), Lecture Notes in Pure and Applied Mathematics 163, Marcel Dekker, New York, pp 1-12
4. Acquistapace P, Flandoli F, Terreni B (1991), Initial boundary value problems and optimal control for nonautonomous parabolic systems, SIAM J Control Optim 29:89-118
5. Acquistapace P, Terreni B (1987), A unified approach to abstract linear non-autonomous parabolic equations, Rend Sem Mat Univ Padova 78:47-107
6. Acquistapace P, Terreni B (1986), On fundamental solutions for abstract parabolic equations, in Differential Equations in Banach Spaces (proceedings, Bologna, 1985) (Favini A, Obrecht E, editors), Lecture Notes in Mathematics 1223, Springer-Verlag, Berlin, pp 1-11
7. Acquistapace P, Terreni B (1992), Regularity properties of the evolution operator for abstract linear parabolic equations, Diff Int Eq 5:1151-1184
8. Acquistapace P, Terreni B (1996), Infinite horizon LQR problems for non-autonomous parabolic systems with boundary control, SIAM J Control Optim 34:1-30
9. Acquistapace P, Terreni B (1999), Classical solutions of nonautonomous Riccati equations arising in parabolic boundary control problems, Appl Math Optim 39:361-409
10. Agmon, S, Douglis A, Nirenberg L (1964), Estimates near the boundary of solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm Pure Appl Math 17:35-92
11. Balakrishnan VA (1978), Boundary control of parabolic equations: L-Q-R theory, in Theory of Nonlinear Operators (proceedings 5th International Summer School, Berlin, 1977) (Kluge R, editor), Abhandlungen der Akademie der Wissenschafter des DDR, Abteilung Mathematik, Naturwissenschaften und Tecknik 6H, Akademie-Verlag, Berlin, pp 11-23
12. Bensoussan A, Da Prato G, Delfour MC, Mitter SK (1993), Representation and Control of Infinite Dimensional Systems, vol II, Birkhäuser, Boston
13. Curtain R, Pritchard AJ (1976), Infinite-dimensional Riccati equation for systems defined by evolution operators, SIAM J Control Optim 14:951-983
14. Da Prato G (1973), Quelques résultats d'existence, unicité et regularité pour un problème de la théorie du contrôle, J Math Pures Appl 52:353-375
15. Da Prato G, Ichikawa A (1985), Riccati equations with unbounded coefficients, Ann Mat Pura Appl 140:209-221
16. Da Prato G, Ichikawa A (1990), Quadratic control for linear time-varying systems, SIAM J Control Optim 28:359-381
17. Delfour MC, Sorine M (1983), The linear quadratic optimal control problem for parabolic systems with boundary control through a Dirichlet condition, in Control of Distributed Parameter Systems (proceedings, 3rd IFAC Symposium, Toulouse, 1982) (Babary JP, Le Letty L, editors), Pergamon Press, Oxford, pp 87-90
18. Flandoli F (1984), Riccati equation arising in a boundary control problem with distributed parameters, SIAM J Control Optim 22:76-86
19. Flandoli F (1987), Algebraic Riccati equation arising in boundary control problems, SIAM J Control Optim 25:612-636
20. Flandoli F (1990), A counterexample in the boundary control of parabolic systems, Appl Math Lett 3:47-50
21. Flandoli F (1992), On the direct solution of Riccati equations arising in boundary control theory, Ann Mat Pura Appl 163:93-131
22. Hardy GH, Littlewood JE, Polya G (1934), Inequalities, Cambridge University Press, Cambridge
23. Lasiecka I, Triggiani R (1983), Dirichlet boundary control problem for parabolic equations with quadratic cost: analiticity and Riccati's feedback synthesis, SIAM J Control Optim 21:41-67
24. Lasiecka I, Triggiani R (1991), Differential and Algebraic Riccati Equations with Application to Boundary Point Control Problems: Continuous Theory and Approximation Theory, Lecture Notes in Control and Information Science 164, Springer-Verlag, Berlin
25. Lasiecka I, Triggiani R (1992), Riccati differential equations with unbounded coefficients and non-smooth terminal condition: the case of analytic semigroups, SIAM J Math Anal 23:449-481
26. Lasiecka I, Triggiani R (1994), Further regularity properties in quadratic cost problems for parabolic equations with boundary control and non-smoothing final state penalization, in Optimal Control of Differential Equations (proceedings Festschrift in honor of C Corduneanu, Athens, 1993) (Pavel NH, editor), Lecture Notes in Pure and Applied Mathematics 160, Marcel Dekker, New York, pp 173-194
27. Lions JL (1972), Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin
28. Lunardi A (1995), Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel
29. Sinestrari E (1985), On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J Math Anal Appl 107:16-66
30. Sobolevskii PE (1964), Coerciveness inequalities for abstract parabolic equations, Soviet Math Dokl 20(II):894-897