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Related Experiment Videos

Hamilton-Jacobi-Bellman equations and approximate dynamic programming on time scales.

John Seiffertt¹, Suman Sanyal, Donald C Wunsch

¹Applied Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA. jes0b4@mst.edu

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society

|July 18, 2008

Summary

This study extends the time scales calculus to approximate dynamic programming, enabling new mathematical approaches for complex problems. The research bridges calculus of time scales and stochastic control for broader applications.

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Area of Science:

Mathematics
Applied Mathematics
Dynamic Systems

Background:

The calculus of time scales is an emerging mathematical field with broad multidisciplinary potential.
Approximate dynamic programming (ADP) is a powerful technique for solving complex control problems.

Purpose of the Study:

To extend the calculus of time scales to approximate dynamic programming.
To develop new mathematical frameworks for dynamic programming on isolated time scales.

Main Methods:

Extending the backward induction algorithm of dynamic programming to all isolated time scales.
Motivating and proving Hamilton-Jacobi-Bellman equations on time scales.

Main Results:

The traditional discrete dynamic programming is generalized to the time scales calculus.
Hamilton-Jacobi-Bellman equations are established and proven on time scales.

Conclusions:

This work connects the calculus of time scales with stochastic control via ADP.
The findings open new avenues for research in both theoretical mathematics and applied control theory.