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.
Fractional Order Version of the Hamilton–Jacobi–Bellman Equation
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 29, 2018; final manuscript received October 30, 2018; published online November 28, 2018. Assoc. Editor: Dumitru Baleanu.
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Razminia, A., Asadizadehshiraz, M., and Torres, D. F. M. (November 28, 2018). "Fractional Order Version of the Hamilton–Jacobi–Bellman Equation." ASME. J. Comput. Nonlinear Dynam. January 2019; 14(1): 011005. https://doi.org/10.1115/1.4041912
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