Hamilton-Jacobi-Bellman equation of nonlinear optimal control problems with fractional discounted cost
Gou Nishida, Takahiro Takamatsu, Noboru Sakamoto · IFAC-PapersOnLine · 2025
This paper derives a Hamilton-Jacobi-Bellman equation for nonlinear optimal control problems that minimize cost functions with fractional discounted costs, based on Bellman’s principle of optimality. The exponential function is used as the discounted cost in conventional optimal control problems. The fractional discounted cost is described by the Mittag-Leffler function, which can be considered a generalized exponential function and is used in the solutions of fractional dynamical systems. The Mittag-Leffler function can describe gradual changes in the weights of cost functions with respect to time evolution, compared to exponential functions.