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

• Autorzy: K. Maciej Przyłuski
• Języki publikacji: EN

Abstrakty

EN

In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.

Słowa kluczowe

EN

minimum norm problem; linear-quadratic control; linear-quadratic economies; controllability; continuity of optimal control

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2014
• Tom: 24
• Numer: 4
• Strony: 723-733

Daty

wydano

2014

otrzymano

2013-09-30

poprawiono

2014-05-07

Twórcy

autor

K. Maciej Przyłuski

• Department of Applied Sciences, Collegium Mazovia, ul. Sokołowska 116, 08-110 Siedlce, Poland

Bibliografia

• 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.
• Aubin, J.-P. (2000). Applied Functional Analysis, Wiley, New York, NY.
• Balakrishnan, A.V. (1981). Applied Functional Analysis, Springer, New York, NY.
• Brockett, R.F. (1970). Finite-Dimensional Linear Systems, Wiley, New York, NY.
• Chow, G.P. (1976). Analysis and Control of Dynamic Economic Systems, Wiley, New York, NY.
• Corless, M.J. and Frazho, A.E. (2003). Linear Systems and Control. An Operator Perspective, Marcel Dekker, New York, NY.
• 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.
• Curtain, R.F. and Pritchard A.J. (1978). Infinite-Dimensional Linear Systems Theory, Springer, Berlin.
• Curtain, R.F. and Zwart H. (1995). An Introduction to InfiniteDimensional Linear Systems Theory, Springer, New York, NY.
• 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.
• Emirsajłow, Z. (1989). Feedback control in LQCP with a terminal inequality constraint, Journal of Optimization Theory and Applications 62(3): 387-403.
• Evans, L.C. (2010). Partial Differential Equations, American Mathematical Society, Providence RI.
• Federico, S. (2011). A stochastic control problem with delay arising in a pension fund model, Finance and Stochastics 15(3): 421-459.
• 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.
• 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.
• Kendrick, D.A. (1981). Stochastic Control for Economic Models, McGraw-Hill, New York, NY.
• Kobayashi, T. (1978). Some remarks on controllability for distributed parameter systems, SIAM Journal on Control and Optimization 16(5): 733-742.
• Laurent, P.-J. (1972). Approximation et Optimisation, Hermann, Paris.
• Ljungqvist, L. and Sargent, T.J. (2004). Recursive Macroeconomic Theory, MIT Press, Cambridge, MA.
• Luenberger, D.G. (1969). Optimization by Vector Space Methods, Wiley, New York, NY.
• 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.
• Porter, W.A. (1966). Modern Foundations of System Engineering, Macmillan, New York, NY.
• 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.
• Rolewicz, S. (1987). Functional Analysis and Control Theory. Linear Systems, PWN, Warsaw, (in Polish).
• Sent, E.-M. (1998). The Evolving Rationality of Rational Expectations: An Assessment of Thomas Sargent's Achievements, Cambridge University Press, Cambridge.
• 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.
• 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.
• 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.

Identyfikatory

DOI

10.2478/amcs-2014-0053