Turnpike properties of approximate solutions of autonomous variational problems

• Autorzy: Zaslavski A. J.
• Języki publikacji: EN

Abstrakty

EN

In this work we study the structure of approximate solutions of autonomous variational problems with vector-valued functions. We are interested in turnpike properties of these solutions, which are independent of the length of the interval, for all sufficiently large intervals. We show that the turnpike properties are stable under small perturbations of integrands.

Słowa kluczowe

EN

good function; infinite horizon problem; integrand; turnpike property

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2008
• Tom: Vol. 37, no 2
• Strony: 491--512
• Opis fizyczny: Bibliogr. 30 poz.

Twórcy

autor

Zaslavski A. J.

• Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel,

Bibliografia

• ANDERSON, B.D.O. and MOORE, J.B. (1971) Linear Optimal Control. Prentice-Hall, Englewood Cliffs, NJ.
• ATSUMI, H. (1965) Neoclassical growth and the efficient program of capital accumulation. Review of Economic Studies 32, 127-136.
• AUBRY, S. and LE DAERON, P.Y. (1983) The discrete Frenkel-Kontorova model and its extensions I. Physica D 8, 381-422.
• BELKINA, T.A. and ROTAR, V.I. (2006) On optimality in probability and almost surely for processes with connectivity property. I. The discrete-time case. Probab. Appl. 50, 16-33.
• BLOT, J. and CARTIGNY, P. (2000) Optimality in infinite-horizon variational problems under sign conditions. J. Optim. Theory Appl. 106, 411-419.
• BLOT, J. and CRETEZZ, B. (2004) On the smoothness of optimal paths. Decis. Econ. Finance 27, 1-34.
• BLOT, J. and MICHEL, P. (2003) The value-function of an infinite-horizon linear quadratic problem. Appl. Math. Lett. 16, 71-78.
• COLEMAN, B.D., MARCUS, M. and MIZEL, V.J. (1992) On the thermodynamics of periodic phases. Arch. Rational Mech. Anal. 117, 321-347.
• GALE, D. (1967) On optimal development in a multi-sector economy. Review of Economic Studies 34, 1-18.
• GLIZER, V. and SHINAR, J. (1993) On the structure of a class of time-optimal trajectories. Optimal Control Appl. Methods 14, 271-279.
• LEIZAROWITZ, A. (1985) Infinite horizon autonomous systems with unbounded cost. Appl Math, and Opt. 13, 19-43.
• LEIZAROWITZ, A. (1986) Tracking nonperiodic trajectories with the overtaking criterion. Appl. Math, and Opt. 14, 155-171.
• LEIZAROWITZ, A. and MIZEL, V.J. (1989) One dimensional infinite horizon variational problems arising in continuum mechanics. Arch. Rational Mech. Anal. 106, 161-194.
• MAKAROV, V.L. and RUBINOV, A.M. (1977) Mathematical Theory of Economic Dynamics and Equilibria. Springer-Verlag, New York.
• MARCUS, M. and ZASLAVSKI, A.J. (1999) The structure of extremals of a class of second order variational problems. Ann. Inst. H. Poincare, Anal. Non Lineaire 16, 593-629.
• MARCVS, M. and ZASLAVSKJ, A.J. (2002) The structure and limiting behavior of locally optimal minimizers. Ann. Inst. H. Poincare, Anal. Non Lineaire 19, 343-370.
• MCKENZlE, L.W. (2002) Classical General Equilibrium Theory. The MIT Press, Cambridge, Massachusetts.
• MORDUKHOVICH, B. (1990) Minimax design for a class of distributed parameter systems. Automat. Remote Control 50, 1333-1340.
• MORDUKHOVICH, B. and SHVARTSMAN, I. (2004) Optimization and feedback control of constrained parabolic systems under uncertain perturbations. Optimal Control, Stabilization and Nonsmooth Analysis, Lecture Notes Control Inform. Sci. Springer, 121-132.
• PICKENHAIN, S. and LUKINA, V. (2006) Sufficiency conditions for infinite horizon optimal control problems. Recent Advances in Optimization. Proceedings of the 12th French-German-Spanish Conference on Optimization, Avignon. Springer, 217-232.
• SAMUELSON, P.A. (1965) A catenary turnpike theorem involving consumption and the golden rule. American Economic Review 55, 486-496.
• WEIZSACKER, C.C. (1965) Existence of optimal programs of accumulation for an infinite horizon. Rev. Econ. Studies 32, 85-104.
• ZASLAVSKI, A.J. (1987) Ground states in Frenkel-Kontorova model. Math. USSR Izvestiya 29, 323-354.
• ZASLAVSKI, A.J. (1996) Dynamic properties of optimal solutions of variational problems. Nonlinear Analysis: Theory, Methods and Applications 27, 895-931.
• ZASLAVSKI, A.J. (1997) Turnpike property of optimal solutions of infinite horizon variational problems. SIAM Journal on Control and Optimization 35, 1169-1203.
• ZASLAVSKI, A.J. (1998) Existence and uniform boundedness of optimal solutions of variational problems. Abstract and Applied Analysis 3, 265-292.
• ZASLAVSKI, A.J. (1999) Turnpike property for extremals of variational problems with vector-valued functions. Transactions of the AMS 351, 211-231.
• ZASLAVSKI, A.J. (2000) The turnpike property for extremals of nonautonomous variational problems with vector-valued functions. Nonlinear Analysis 42, 1465-1498.
• ZASLAVSKI, A.J. (2005) Turnpike Properties in the Calculus of Variations and Optimal Control. Springer, New York.
• ZASLAVSKI, A.J. (2007) Structure of extremals of autonomous convex variational problems. Nonlinear Analysis: Real World Applications 8, 1186-1207.