Reinforcement learning and adaptive dynamic programming for feedback control
IEEE Circuits and Systems Magazine
An alpha derivative formulation of the Hamilton-Jacobi-Bellman equation of dynamic programming
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Adaptive dynamic programming: an introduction
IEEE Computational Intelligence Magazine
Backpropagation and ordered derivatives in the time scales calculus
IEEE Transactions on Neural Networks
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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.