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On a generalization of the impulsive control concept: Controlling system jumps

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  • This paper concerns the investigation of a general impulsive control problem. The considered impulsive processes are of non-standard type: control processes admit ordinary type controls as the impulse develops. New necessary conditions of optimality in the form of Pontryagin Maximum Principle are obtained. These conditions are applied to a model problem and are shown to yield useful information about optimal control modes.
    Mathematics Subject Classification: Primary: 49N25.


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  • [1]

    A. V. Arutyunov, "Optimality Conditions: Abnormal and Degenerate Problems," Math. Appl., Kluwer Academic Publisher, 2000.


    A. V. Arutyunov, D. Yu. Karamzin and F. L. Pereira, A nondegenerate maximum principle for the impulse control problem with state constraints, SIAM J. Control Optim., 43 (2005), 1812-1843.doi: doi:10.1137/S0363012903430068.


    A. V. Arutyunov and D. Yu. Karamzin, Necessary conditions for minimum in impulsive control problems, Nonlinear Dynamics and Control, Moscow, Fizmatlit, (2004), 205-240, (in Russian).


    A. V. Arutyunov, D. Yu. Karamzin, and F. L. Pereira, On constrained impulsive control problems, Sovremennaya Matematika i Ee Prilozheniya, 65 (2009) (in Russian, the English translation in Journal of Mathematical Sciences, 165 (2010), 654-687).


    A. Bressan and F. Rampazzo, On differential systems with vector-valued impulsive controls, Boll. Un. Matematica Italiana B, 2 (1988), 641-656.


    A. Bressan and F. Rampazzo, Impulsive control systems with commutative vector fields, J. Optim. Theory and Appl., 71 (1991), 67-83.doi: doi:10.1007/BF00940040.


    V. A. Dykhta and O. N. Samsonyuk, "Optimal Impulse Control and Applications," Fizmatlit, Moscow, 2000, (in Russian).


    N. N. Krasovski, "The Theory of Motion Control," Nauka, Moscow, 1968, (in Russian)


    A. B. Kurzhanski., Optimal systems with impulse controls, in "Differential Games and Control Problems," UNC AN SSSR. Sverdlovsk, 1975, (in Russian).


    A. B. Kurzhanski and A. N. Daryin, Dynamic programming for impulse controls, Annual Reviews in Control, 32 (2008), 213-227.doi: doi:10.1016/j.arcontrol.2008.08.001.


    F. L. Pereira and G. N. Silva, Necessary conditions of optimality for vector-valued impulsive control problems, Systems and Control Letters, 40 (2000), 205-215.doi: doi:10.1016/S0167-6911(00)00027-X.


    L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes," Gordon and Beach, New York, 1986.


    R. W. Rishel, An extended Pontryagin principle for control systems, whose control laws contain measures, J. SIAM. Ser. A. Control, 3 (1965), 191-205.


    G. N. Silva and R. B. Vinter, Measure differential inclusions, J. Math. Anal. Appl., 202 (1996), 727-746.doi: doi:10.1006/jmaa.1996.0344.


    R. B. Vinter and F. L. Pereira, A maximum principle for optimal processes with discontinuous trajectories, SIAM J. Control Optim., 26 (1988), 205-229.doi: doi:10.1137/0326013.

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