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Avtomat. i Telemekh., 2011, Issue 6, Pages 48–63 (Mi at2223)  

This article is cited in 3 scientific papers (total in 3 papers)

Intellectual Control Systems

Positional solutions of Hamilton–Jacobi equations in control problems for discrete-continuous systems

V. A. Dykhta, S. P. Sorokin

Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia

Abstract: We develop a canonical global optimality theory based on operating with the set of solutions for the Hamilton–Jacobi inequalities that parametrically depend on the initial (or final) position. These solutions, called positional $L$-functions (of Lyapunov type), naturally arise in the studies of control problems for discrete-continuous (hybrid, impulse) systems; an important prototype of such problems are classical optimal control problems with general end constraints on the trajectory. We analyze sufficient optimality conditions with this new class of $L$-functions and invert the maximum principle into a sufficient condition for nonlinear problems of optimal impulse control.

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English version:
Automation and Remote Control, 2011, 72:6, 1184–1198

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Presented by the member of Editorial Board: . . 

Received: 16.12.2010

Citation: V. A. Dykhta, S. P. Sorokin, “Positional solutions of Hamilton–Jacobi equations in control problems for discrete-continuous systems”, Avtomat. i Telemekh., 2011, no. 6, 48–63; Autom. Remote Control, 72:6 (2011), 1184–1198

Citation in format AMSBIB
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\paper Positional solutions of Hamilton--Jacobi equations in control problems for discrete-continuous systems
\jour Avtomat. i Telemekh.
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\pages 48--63
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\transl
\jour Autom. Remote Control
\yr 2011
\vol 72
\issue 6
\pages 1184--1198
\crossref{https://doi.org/10.1134/S0005117911060051}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dykhta V.A., Sorokin S.P., Yakovenko G.N., “Upravlyaemye sistemy: usloviya ekstremalnosti, optimalnosti i identifikatsiya algebraicheskoi struktury”, Trudy Moskovskogo fiziko-tekhnicheskogo instituta, 3:3 (2011), 122–131  elib
    2. S. P. Sorokin, “Monotonnye funktsii tipa Lyapunova i usloviya globalnoi optimalnosti dlya zadach upravleniya diskretnymi sistemami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 4:3 (2011), 132–145  mathnet
    3. S. P. Sorokin, “Bipozitsionnye resheniya neravenstv Gamiltona–Yakobi v neklassicheskikh lineino-kvadratichnykh zadachakh optimalnogo upravleniya”, Programmnye sistemy: teoriya i prilozheniya, 3:5 (2012), 33–44  mathnet
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