Read e-book online Adaptive Dynamic Programming with Applications in Optimal PDF

By Derong Liu, Qinglai Wei, Ding Wang, Xiong Yang, Hongliang Li

ISBN-10: 331950813X

ISBN-13: 9783319508139

ISBN-10: 3319508156

ISBN-13: 9783319508153

This publication covers the newest advancements in adaptive dynamic programming (ADP). The textual content starts with a radical heritage evaluation of ADP to ensure that readers are sufficiently conversant in the basics. within the center of the publication, the authors handle first discrete- after which continuous-time platforms. assurance of discrete-time platforms begins with a extra normal type of worth new release to illustrate its convergence, optimality, and balance with entire and thorough theoretical research. A extra lifelike kind of price generation is studied the place worth functionality approximations are assumed to have finite error. Adaptive Dynamic Programming additionally information one other road of the ADP process: coverage generation. either uncomplicated and generalized kinds of policy-iteration-based ADP are studied with entire and thorough theoretical research by way of convergence, optimality, balance, and blunder bounds. between continuous-time platforms, the keep watch over of affine and nonaffine nonlinear platforms is studied utilizing the ADP method that is then prolonged to different branches of regulate thought together with decentralized keep watch over, powerful and assured price keep an eye on, and online game concept. within the final a part of the ebook the real-world importance of ADP conception is gifted, concentrating on 3 program examples built from the authors’ work:

• renewable power scheduling for clever energy grids;• coal gasification approaches; and• water–gas shift reactions.
Researchers learning clever keep an eye on tools and practitioners seeking to follow them within the chemical-process and power-supply industries will locate a lot to curiosity them during this thorough remedy of a complicated method of control.

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Extra resources for Adaptive Dynamic Programming with Applications in Optimal Control

Sample text

Vi+1 (x) = − R−1 (x)gT (x) 2 dx The following results were shown in [72, 73]. 3 Adaptive Dynamic Programming 21 (1) The sequence of functions {Vi } obtained above converges to the optimal cost function J ∗ . 23), for all i = 0, 1, . . (3) Each of the value functions Vi+1 (x) is a Lyapunov function of the plant, for all i = 0, 1, . . 23) with the following value function ∞ V (x(t)) = ∞ U(x(τ ), u(τ ))dτ = t x T(τ )Qx(τ ) + uT(τ )Rx(τ ) dτ, t where Q and R are positive-definite matrices. The successive approximation to the HJB equation starts with an initial stabilizing control law v0 (x).

22), one will get a sequence of functions Vi . This sequence {Vi } will converge to the bound V (or V ) of the cost function J ∗ . Consequently, ui will approximate the optimal control when i tends to ∞. It is important to note that the sequences {Vi } and {ui } are obtainable by computation and they approximate the optimal cost and the optimal control law, respectively. Some further theoretical results for ADP have been obtained in [72, 73]. These works investigated the stability and optimality for some special cases of ADP.

25) repeatedly, one will get sequences of estimations of the optimal cost function J ∗ and the optimal control u∗ . Starting from an initial stabilizing control v0 (x), for i = 0, 1, . . , the approximation is given by the following iterations between value functions ∞ Vi+1 (x) = U(x(τ ), vi (τ ))dτ t and control laws dVi+1 (x) 1 . vi+1 (x) = − R−1 (x)gT (x) 2 dx The following results were shown in [72, 73]. 3 Adaptive Dynamic Programming 21 (1) The sequence of functions {Vi } obtained above converges to the optimal cost function J ∗ .

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Adaptive Dynamic Programming with Applications in Optimal Control by Derong Liu, Qinglai Wei, Ding Wang, Xiong Yang, Hongliang Li

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