On an infinite dimensional linear-quadratic problem with fixed endpoints: the continuity question

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1. Athans, M. (1971). The role and use of the stochastic linear-quadratic-Gaussian problem in control system design, IEEE Transactions on Automatic Control, AC16(6): 529-552. 
2. Aubin, J.-P. (2000). Applied Functional Analysis, Wiley, New York, NY. 
3. Balakrishnan, A.V. (1981). Applied Functional Analysis, Springer, New York, NY. Zbl0459.46014
4. Brockett, R.F. (1970). Finite-Dimensional Linear Systems, Wiley, New York, NY. Zbl0216.27401
5. Chow, G.P. (1976). Analysis and Control of Dynamic Economic Systems, Wiley, New York, NY. 
6. Corless, M.J. and Frazho, A.E. (2003). Linear Systems and Control. An Operator Perspective, Marcel Dekker, New York, NY. Zbl1050.93001
7. Curtain, R.F. (1984). Linear-quadratic control problem with fixed endpoints in infinite dimensions, Journal of Optimization Theory and Its Applications 44(1): 55-74. Zbl0527.93037
8. Curtain, R.F. and Pritchard A.J. (1978). Infinite-Dimensional Linear Systems Theory, Springer, Berlin. Zbl0389.93001
9. Curtain, R.F. and Zwart H. (1995). An Introduction to InfiniteDimensional Linear Systems Theory, Springer, New York, NY. Zbl0839.93001
10. Douglas, R.G. (1966). On majorization, factorization, and range inclusion of operators on Hilbert space, Proceedings of the American Mathematical Society 18(2): 413-415. Zbl0146.12503
11. Emirsajłow, Z. (1989). Feedback control in LQCP with a terminal inequality constraint, Journal of Optimization Theory and Applications 62(3): 387-403. Zbl0654.93035
12. Evans, L.C. (2010). Partial Differential Equations, American Mathematical Society, Providence RI. Zbl1194.35001
13. Federico, S. (2011). A stochastic control problem with delay arising in a pension fund model, Finance and Stochastics 15(3): 421-459. Zbl1302.93238
14. Fuhrmann, P.A. (1972). On weak and strong reachability and controllability of infinite-dimensional linear systems, Journal of Optimization Theory and Its Applications 9(2): 77-89. Zbl0215.30203
15. Kandilakis, D. and Papageorgiou, N.S. (1992). Evolution inclusions of the subdifferential type depending on a parameter, Commentationes Mathematicae Universitatis Carolinae 33(3): 437-449. Zbl0770.34016
16. Kendrick, D.A. (1981). Stochastic Control for Economic Models, McGraw-Hill, New York, NY. Zbl0478.93003
17. Kobayashi, T. (1978). Some remarks on controllability for distributed parameter systems, SIAM Journal on Control and Optimization 16(5): 733-742. Zbl0408.35013
18. Laurent, P.-J. (1972). Approximation et Optimisation, Hermann, Paris. Zbl0238.90058
19. Ljungqvist, L. and Sargent, T.J. (2004). Recursive Macroeconomic Theory, MIT Press, Cambridge, MA. 
20. Luenberger, D.G. (1969). Optimization by Vector Space Methods, Wiley, New York, NY. Zbl0176.12701
21. Papageorgiou, N.S. (1991). On the dependence of the solutions and optimal solutions of control problems on the control constraint set, Journal of Mathematical Analysis and Applications 158(2): 427-447. Zbl0741.49003
22. Porter, W.A. (1966). Modern Foundations of System Engineering, Macmillan, New York, NY. 
23. Przyłuski, K.M. (1981). Remarks on continuous dependence of an optimal control on parameters, in O. Moeschlin and D. Pallaschke (Eds.), Game Theory and Mathematical Economics, North-Holland, Amsterdam, pp. 333-337. Zbl0475.49025
24. Rolewicz, S. (1987). Functional Analysis and Control Theory. Linear Systems, PWN, Warsaw, (in Polish). Zbl0633.93002
25. Sent, E.-M. (1998). The Evolving Rationality of Rational Expectations: An Assessment of Thomas Sargent's Achievements, Cambridge University Press, Cambridge. 
26. Triggiani, R. (1975a). A note on the lack of exact controllability for mild solutions in Banach spaces, SIAM Journal on Control and Optimization 15(3): 407-411. Zbl0354.93014
27. Triggiani, R. (1975b). On the lack of exact controllability for mild solutions in Banach spaces, Journal of Mathematical Analysis and Applications 50(2): 438-446. Zbl0305.93013
28. Triggiani, R. (1976). Extensions of rank conditions for controllability and observability to Banach spaces and unbounded operators, SIAM Journal on Control and Optimization 14(2): 313-338. Zbl0326.93003