Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111580
 Title: Dynamic Programming Principle and Hamilton-jacobi-bellman Equations for Fractional-order Systems Authors: Gomoyunov, M. I. Issue Date: 2020 Publisher: Society for Industrial and Applied Mathematics PublicationsSociety for Industrial & Applied Mathematics (SIAM) Citation: Gomoyunov M. I. Dynamic Programming Principle and Hamilton-jacobi-bellman Equations for Fractional-order Systems / M. I. Gomoyunov // SIAM Journal on Control and Optimization. — 2020. — Vol. 58. — Iss. 6. — P. 3185-3211. Abstract: We consider a Bolza-type optimal control problem for a dynamical system described by a fractional differential equation with the Caputo derivative of an order \alpha \in (0, 1). The value of this problem is introduced as a functional in a suitable space of histories of motions. We prove that this functional satisfies the dynamic programming principle. Based on a new notion of coinvariant derivatives of the order \alpha, we associate the considered optimal control problem with a Hamilton-Jacobi-Bellman equation. under certain smoothness assumptions, we establish a connection between the value functional and a solution to this equation. Moreover, we propose a way of constructing optimal feedback controls. The paper concludes with an example. © 2020 Society for Industrial and Applied Mathematics. Keywords: COINVARIANT DERIVATIVESDYNAMIC PROGRAMMING PRINCIPLEFEEDBACK CONTROLFRACTIONAL DERIVATIVESHAMILTON-JACOBI-BELLMAN EQUATIONOPTIMAL CONTROLCONTROL THEORYDIFFERENTIAL EQUATIONSDYNAMICAL SYSTEMSFUNCTIONAL PROGRAMMINGOPTIMAL CONTROL SYSTEMSCAPUTO DERIVATIVESDYNAMIC PROGRAMMING PRINCIPLEFRACTIONAL DIFFERENTIAL EQUATIONSFRACTIONAL-ORDER SYSTEMSHAMILTON JACOBI BELLMAN EQUATIONOPTIMAL CONTROL PROBLEMOPTIMAL FEEDBACK CONTROLDYNAMIC PROGRAMMING URI: http://hdl.handle.net/10995/111580 Access: info:eu-repo/semantics/openAccess SCOPUS ID: 85096803709 PURE ID: 20220945 ISSN: 0363-0129 metadata.dc.description.sponsorship: This work was supported by the RSF, project 19-71-00073. RSCF project card: 19-71-00073 Appears in Collections: Научные публикации, проиндексированные в SCOPUS и WoS CC

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