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By Derong Liu, Qinglai Wei, Ding Wang, Xiong Yang, Hongliang Li
This publication covers the newest advancements in adaptive dynamic programming (ADP). The textual content starts with an intensive historical past assessment of ADP with the intention that readers are sufficiently accustomed to the basics. within the center of the ebook, the authors tackle first discrete- after which continuous-time platforms. assurance of discrete-time platforms begins with a extra normal kind of price new release to illustrate its convergence, optimality, and balance with entire and thorough theoretical research. A extra practical kind of worth generation is studied the place worth functionality approximations are assumed to have finite blunders. Adaptive Dynamic Programming additionally info one other street of the ADP technique: coverage new release. either simple and generalized different types of policy-iteration-based ADP are studied with entire and thorough theoretical research when it comes to convergence, optimality, balance, and blunder bounds. between continuous-time structures, the keep an eye on of affine and nonaffine nonlinear structures is studied utilizing the ADP procedure that is then prolonged to different branches of keep an eye on conception together with decentralized keep an eye on, strong and warranted expense keep watch over, and online game concept. within the final a part of the booklet the real-world value of ADP idea is gifted, targeting 3 program examples built from the authors’ work:
• renewable power scheduling for shrewdpermanent strength grids;• coal gasification procedures; and• water–gas shift reactions.
Researchers learning clever keep an eye on equipment and practitioners seeking to practice them within the chemical-process and power-supply industries will locate a lot to curiosity them during this thorough therapy of a sophisticated method of control.
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Additional info for Adaptive Dynamic Programming with Applications in Optimal Control
Example text
Note that the optimal control sequence depends on xk+1 . 1). According to Bellman, the optimal cost from time k on is equal to J ∗ (xk ) = min{U(xk , uk ) + γ J ∗ (xk+1 )} = min{U(xk , uk ) + γ J ∗ (F(xk , uk ))}. , uk∗ = arg min{U(xk , uk ) + γ J ∗ (xk+1 )}. 4) is the principle of optimality for discrete-time systems. Its importance lies in the fact that it allows one to optimize over only one control vector at a time by working backward in time. Dynamic programming is a very useful tool in solving optimization and optimal control problems.
First, the theory and computational methods on discounted problems are developed. The computational methods for generalized discounted dynamic programming, including the asynchronous optimistic policy iteration and its application to game and minimax problems, constrained policy iteration, and Q-learning are provided. Then, the stochastic shortest path problems, the undiscounted problems, and the average cost per stage problems are also discussed. The policy iteration methods and the asynchronous optimistic versions for stochastic shortest path problems that involve improper policies are given.
The only difference is the definition of reward function. 15), it is defined as rt+1 = r(st , at , st+1 ), whereas in Fig. 2, it is defined as Uk = U(xk , uk ), where the current times are t and k, respectively. We will make clear Fig. 3 Adaptive Dynamic Programming 13 Fig. 3 Backward-in-time approach Uk Jk Critic Network xk Ek 1 1 Copied Jk Critic Network xk later the reason behind this one-step time difference between rt+1 and Uk . 23), the same learning objective is utilized. However, in TD and TD(λ), the update of value functions at each step only makes a move according to the step size toward the target, and presumably, it does not reach the target.