Fractional Order Version of the HJB Equation

[+] Author and Article Information
Abolhassan Razminia

Ph.D. in Control Systems, Associate Professor, Electrical Engineering Department, School of Engineering, Persian Gulf University, P. O. Box 75169, Bushehr, Iran

Mehdi AsadiZadehShiraz

M.Sc. in Control Systems, Electronic and Electrical Engineering Department, Shiraz University of Technology, P. O. Box 71555-313, Shiraz, Iran

Delfim F. M. Torres

Ph.D. and D.Sc. (Habilitation) in Mathematics, Full Professor, Coordinator of the R&D Unit CIDMA, Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro 3810-193, Portugal

1Corresponding author.

ASME doi:10.1115/1.4041912 History: Received June 29, 2018; Revised October 30, 2018


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.

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