Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Neuro-Dynamic Programming
Partial differential equations on time scales
Journal of Computational and Applied Mathematics - Dynamic equations on time scales
Chain rule and invariance principle on measure chains
Journal of Computational and Applied Mathematics - Dynamic equations on time scales
Handbook of Learning and Approximate Dynamic Programming (IEEE Press Series on Computational Intelligence)
Stability for time varying linear dynamic systems on time scales
Journal of Computational and Applied Mathematics
Partial dynamic equations on time scales
Journal of Computational and Applied Mathematics
Double integral calculus of variations on time scales
Computers & Mathematics with Applications
Approximate Dynamic Programming: Solving the Curses of Dimensionality (Wiley Series in Probability and Statistics)
Hamilton–Jacobi–Bellman Equations and Approximate Dynamic Programming on Time Scales
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Nonregressivity in switched linear circuits and mechanical systems
Mathematical and Computer Modelling: An International Journal
An application of time scales to economics
Mathematical and Computer Modelling: An International Journal
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The time scales calculus, which includes the study of the alpha derivative, is an emerging key area in mathematics. We extend this calculus to Approximate Dynamic Programming. In particular, we investigate application of the alpha derivative, one of the fundamental dynamic derivatives of time scales. We present a alpha-derivative based derivation and proof of the Hamilton-Jacobi-Bellman equation, the solution of which is the fundamental problem in the field of dynamic programming. By drawing together the calculus of time scales and the applied area of stochastic control via Approximate Dynamic Programming, we connect two major fields of research.