Abstract
In its most general form, the optimal control problem is to find a control vector u(t) that will give an extremal value to a performance index J (called the objective function), when the state of the system being controlled is described by an n-dimensional state vector x = (x 1, x 2, … x n) whose components evolve according to the state equations.
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References
Arrow, K. and Kurz, M., (1971), Public investment, the rate of return, and Optimal Fiscal Policy. Baltimore: John Hopkins Press.
Beltrami, E. (1987), Mathematics for Dynamic Modeling. Academic Press.
Burghes, D., and Graham, A. (1980), Introduction to Control Theory including Optimal Control. Ellis Horwood Series in Mathematics & its Applications, John Wiley and Sons.
Chiarella, Carl. (1990) The elements of a nonlinear theory of economic dynamics. Lecture Notes in Economics and Mathematical Systems vol. 343. Springer.
Dockner, E., Feichtinger, G. (1991) “On the Optimality of Limit Cycles in Dynamic Economic Systems”. Journal of Economics (Zeitschrift fur Nationalokonomie); 53(1), pages 31–50.
Fanchon, P. and Melese, F. (1996). “A Model of Periodic Job Training.” International Advances in Economic Research, vol 2.
Fanchon, P. Rifkin, E. and Sengupta, J. (1987). “A Dynamic and Stochastic Model of Price Leadership.” Developments of Control Theory for Economic Analysis, Carrara and Sartore editors, Martinus Nijhoff (Kluwer), pages 239–260.
Goodwin, R. (1991). “New Results in Non-linear Economic Dynamics”, Economic Systems Research; 3(4), pages 426–27.
Halkin, H. (1974), “Necessary Conditions for Optimal Problems with Infinite Horizons,” Econometrica, vol. 42, pages 267–272.
Michel, P. (1982), “On the Transversality Condition in Infinite Horizon Optimal Problems”, Econometrica, vol. 50, No. 5, pages 975–985.
Seierstad, A. And Sydsaeter, K., (1987), Optimal Control Theory with Economic Applications, North Holland.
Slotine, J. and Li, W., (1991) Applied Non-Linear Control, Prentice Hall.
Pontryagin, L., Boltyanskii, V., Gramklelidze, R. and Mischenko, E. (1962), The Mathematical Theory of Optimal Processes, Wiley (Interscience) New York.
Wirl, F. (1994). “A New Route to Cyclical Strategies in Two-dimensional Optimal Control Models.” Ricerche Economiche; 48(2), pages 165–73.
Wirl, F., (1994). “The Ramsey Model Revisited: The Optimality of Cyclical Consumption and Growth.” Journal of Economics (Zeitschrift fur Nationalokonomie); 60(1), pages 81–98.
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Sengupta, J.K., Fanchon, P. (1997). Continuous time models. In: Control Theory Methods in Economics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6285-6_2
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DOI: https://doi.org/10.1007/978-1-4615-6285-6_2
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