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Full-Text Articles in Engineering
Hamilton-Jacobi-Bellman Equations And Approximate Dynamic Programming On Time Scales, John E. Seiffertt Iv, Suman Sanyal, Donald C. Wunsch
Hamilton-Jacobi-Bellman Equations And Approximate Dynamic Programming On Time Scales, John E. Seiffertt Iv, Suman Sanyal, Donald C. Wunsch
Electrical and Computer Engineering Faculty Research & Creative Works
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.
Issues On Stability Of Adp Feedback Controllers For Dynamical Systems, S. N. Balakrishnan, Jie Ding, F. L. Lewis
Issues On Stability Of Adp Feedback Controllers For Dynamical Systems, S. N. Balakrishnan, Jie Ding, F. L. Lewis
Mechanical and Aerospace Engineering Faculty Research & Creative Works
This paper traces the development of neural-network (NN)-based feedback controllers that are derived from the principle of adaptive/approximate dynamic programming (ADP) and discusses their closed-loop stability. Different versions of NN structures in the literature, which embed mathematical mappings related to solutions of the ADP-formulated problems called “adaptive critics” or “action-critic” networks, are discussed. Distinction between the two classes of ADP applications is pointed out. Furthermore, papers in “model-free” development and model-based neurocontrollers are reviewed in terms of their contributions to stability issues. Recent literature suggests that work in ADP-based feedback controllers with assured stability is growing in diverse forms.
A Quantum Calculus Formulation Of Dynamic Programming And Ordered Derivatives, John E. Seiffertt Iv, Donald C. Wunsch
A Quantum Calculus Formulation Of Dynamic Programming And Ordered Derivatives, John E. Seiffertt Iv, Donald C. Wunsch
Electrical and Computer Engineering Faculty Research & Creative Works
Much recent research activity has focused on the theory and application of quantum calculus. This branch of mathematics continues to find new and useful applications and there is much promise left for investigation into this field. We present a formulation of dynamic programming grounded in the quantum calculus. Our results include the standard dynamic programming induction algorithm which can be interpreted as the Hamilton-Jacobi-Bellman equation in the quantum calculus. Furthermore, we show that approximate dynamic programming in quantum calculus is tenable by laying the groundwork for the backpropagation algorithm common in neural network training. In particular, we prove that the …