title: Hamilton-Jacobi-Bellman equations and approximate dynamic programming on time scales.
abstract: The time scales calculus is a key emerging area of mathematics due to its potential use in a wide variety of multidisciplinary applications. We extend this calculus to approximate dynamic programming (ADP). The core backward induction algorithm of dynamic programming is extended from its traditional discrete case to all isolated time scales. Hamilton-Jacobi-Bellman equations, the solution of which is the fundamental problem in the field of dynamic programming, are motivated and proven on time scales. By drawing together the calculus of time scales and the applied area of stochastic control via ADP, we have connected two major fields of research.
authors.affiliation: Applied Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA. jes0b4@mst.edu
authors.forename: John
authors.initials: J
authors.lastname: Seiffertt
authors.forename: Suman
authors.initials: S
authors.lastname: Sanyal
authors.forename: Donald C
authors.initials: DC
authors.lastname: Wunsch
mesh_terms: D001185:Artificial Intelligence; D003198:Computer Simulation; D005246:Feedback; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D011382:Programming, Linear; D013598:Systems Theory