2018/10/30 by Abolhassan Razminia, Mehdi AsadiZadehShiraz, Mehdi Asadizadehshiraz +1
Computer Science · Engineering · Mathematics · #Advanced Control Systems Design #Extension (predicate logic) #Fractional Differential Equations Solutions #Fractional calculus #Hamilton–Jacobi–Bellman equation #Optimal control #Optimization and Variational Analysis #Order (exchange) #Quantum nonlocality #math.OC #msc:26A33 #msc:49L20 #msc:49M05
paper · pdf · doi:10.1115/1.4041912
published as J. Comput. Nonlinear Dynam. 14 (2019), no. 1, 011005-1--011005-6 · This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Nonlinear Dynamics', ISSN 1555-1415, eISSN 1555-1423, CODEN: JCNDDM. Submitted 28-June-2018; Revised 15-Sept-2018; Accepted 28-Oct-2018
arxiv created 2018/10/30 · openalex created_date 2018/11/09 · openalex publication_date 2018/11/26 · arxiv updated 2018/11/29 · openalex updated_date 2026/08/05
We consider an extension of the well-known Hamilton–Jacobi–Bellman (HJB) equation for fractional order dynamical systems in which a generalized performance index is considered for the related optimal control problem. Owing to the nonlocality of the fractional order operators, the classical HJB equation, in the usual form, does not hold true for fractional problems. Effectiveness of the proposed technique is illustrated through a numerical example.