Optimal control of linear periodic resonant systems in Hilbert spaces

SIAM Journal on Control and Optimization

Volumn 35, Issue 6, 1997, Pages 2137-2156

  Barbu, Viorel ^a  

^a ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

Author keywords

Closed range; Distributed optimal control problems; Maximum principle; p stabilizable

Indexed keywords

DISTRIBUTED PARAMETER CONTROL SYSTEMS; LINEAR CONTROL SYSTEMS; MAXIMUM PRINCIPLE; PROBLEM SOLVING; SYSTEM STABILITY; TIME VARYING CONTROL SYSTEMS;

HILBERT SPACES; LINEAR PERIODIC RESONANT SYSTEMS;

OPTIMAL CONTROL SYSTEMS;

EID: 0031271310     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S036301299529478X     Document Type: Article

References (19)

1. V. BARBU, Analysis and Control of Nonlinear Infinite Dimensional Systems, Academic Press, Boston, 1993.
2. V. BARBU, Optimal control of the one dimensional periodic wave equation, Appl. Math. Optim., 35 (1997), pp. 77-90.
3. V. BARBU, Optimal control of periodic linear systems in Hilbert space, in Proceedings of IFIP Conference on Parameter Distributed Systems, Warsaw, Poland, July 1995.
4. V. BARBU AND T. PRECUPANU, Convexity and Optimization in Banach Spaces, D. Reidel, Dordrecht, the Netherlands, 1986.
5. V. BARBU AND N. PAVEL, Optimal control of periodic systems, Appl. Math. Optim., 33 (1996), pp. 169-188.
6. V. BARBU AND N. PAVEL, Periodic solutions to nonlinear one dimensional wave equation with x-dependent coefficients, Trans. Amer. Math. Soc., to appear.
7. A. BENSOUSSAN, G. DA PRATO, M. DELFOUR, AND S.K. MITTER, Representation and Control of Infinite Dimensional Control Systems, Birkhäuser, Boston, Basel, Berlin, 1993.
8. G. DA PRATO, Synthesis of optimal control for an infinite dimensional periodic problem, SIAM J. Control Optim., 25 (1987), pp. 706-714.
9. A. HARAUX, Nonlinear Evolution Equations-Global Behavior of Solutions, Lecture Notes in Math. 841, Springer-Verlag, Berlin, Heidelberg, New York, 1981.
10. I. LASIECKA AND R. TRIGGIANI, Algebraic Riccati Equations with Applications to Boundary Point Control Problems. Continuous Theory and Approximation Theory, Lecture Notes in Control and Inform. Sci., Springer-Verlag, Berlin, New York, 1991.
11. 2(Γ)-Dirichlet boundary terms, Appl. Math. Optim., 10 (1983), pp. 275-286.
12. J.L. LIONS, Controlabilité exacte, perturbations et stabilisation de systèmes distribués, Tome 1, Masson, Paris, 1988.
13. A. MANITIUS AND R. TRIGGIANI, Function space controllability of linear retarded systems: A derivation from abstract conditions, SIAM J. Control Optim., 16 (1978), pp. 599-645.
14. N. PAVEL, Periodic solutions to nonlinear 2-D wave equations, to appear.
15. 0-semigroup, Trans. Amer. Math. Soc., 284 (1984), pp. 847-857.
16. J. RAUCH AND M. TAYLOR, Exponential decay of solutions to hyperbolic equations in bounded domains, Indiana Univ. Math. J., 24 (1974), pp. 7-86.
17. R.T. ROCKAFELLAR, Existence and duality theorems for convex control problem of Bolza, Trans. Amer. Math. Soc., 159 (1971), pp. 1-40.
18. J.C. SAUT AND B. SCHEURER, Unique continuation for some evolution equations, J. Differential Equations, 66 (1987), pp. 118-139.
19. K. YOSIDA, Functional Analysis, Springer-Verlag, Berlin, Heidelberg, New York, 1977.