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 Publications
Society 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 DERIVATIVES
DYNAMIC PROGRAMMING PRINCIPLE
FEEDBACK CONTROL
FRACTIONAL DERIVATIVES
HAMILTON-JACOBI-BELLMAN EQUATION
OPTIMAL CONTROL
CONTROL THEORY
DIFFERENTIAL EQUATIONS
DYNAMICAL SYSTEMS
FUNCTIONAL PROGRAMMING
OPTIMAL CONTROL SYSTEMS
CAPUTO DERIVATIVES
DYNAMIC PROGRAMMING PRINCIPLE
FRACTIONAL DIFFERENTIAL EQUATIONS
FRACTIONAL-ORDER SYSTEMS
HAMILTON JACOBI BELLMAN EQUATION
OPTIMAL CONTROL PROBLEM
OPTIMAL FEEDBACK CONTROL
DYNAMIC 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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