Integrals of Motion for Discrete-Time Optimal Control Problems

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Torres, Delfim F. M.;
(2003)
  • Subject: Mathematics - Optimization and Control | Mathematical Physics | 39A12 | 49-99

We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the discrete time Lagrangian and discrete... View more
  • References (44)
    44 references, page 1 of 5

    [1] D. Anderson. Noether's theorem in generalized mechanics. J. Phys. A, 6:299-305, 1973. Zbl 0256.49049 MR 54:6786

    [2] A. V. Arutyunov. Optimality conditions. Kluwer Academic Publishers, Dordrecht, 2000. Zbl pre01657516 MR 1845332

    [3] J. C. Baez and J. W. Gilliam. An algebraic approach to discrete mechanics. Lett. Math. Phys., 31(3):205-212, 1994. Zbl 0805.58031 MR 95i:58098

    [4] D. P. Bertsekas. Dynamic programming and optimal control. I. Athena Scientific, Belmont, MA, 2 edition, 2000.

    [5] P. Blanchard and E. Bru¨ning. Variational methods in mathematical physics. Springer-Verlag, Berlin, 1992. Zbl 0756.49023 MR 95b:58049

    [6] G. Blankenstein and A. van der Schaft. Optimal control and implicit Hamiltonian systems. In Nonlinear control in the year 2000, Vol. 1 (Paris), pages 185-205. Springer, London, 2001. MR 1806135

    [7] J. A. Cadzow. Discrete calculus of variations. Int. J. Control, I. Ser., 11:393-407, 1970. Zbl 0193.07601

    [8] J. F. Carin˜ena and H. Figueroa. A geometrical version of Noether's theorem in supermechanics. Rep. Math. Phys., 34(3):277-303, 1994. Zbl 0846.58008 MR 96g:58011

    [9] D. S. Djukic. Noether's theorem for optimum control systems. Internat. J. Control (1), 18:667-672, 1973. Zbl 0281.49009 MR 49:5979

    [10] I. M. Gelfand and S. V. Fomin. Calculus of variations. Dover Publications, Mineola, NY, 2000. Zbl 0964.49001

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