By Derong Liu, Qinglai Wei, Ding Wang, Xiong Yang, Hongliang Li
This booklet covers the newest advancements in adaptive dynamic programming (ADP). The textual content starts with a radical history overview of ADP to ensure that readers are sufficiently acquainted with the basics. within the center of the ebook, the authors deal with first discrete- after which continuous-time structures. assurance of discrete-time structures starts off with a extra normal type of worth generation to illustrate its convergence, optimality, and balance with entire and thorough theoretical research. A extra real looking type of price new release is studied the place worth functionality approximations are assumed to have finite mistakes. Adaptive Dynamic Programming additionally info one other road of the ADP technique: coverage generation. either uncomplicated 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 mistake bounds. between continuous-time structures, the keep watch over of affine and nonaffine nonlinear structures is studied utilizing the ADP technique that's then prolonged to different branches of keep an eye on idea together with decentralized keep watch over, strong and warranted price keep an eye on, and online game conception. within the final a part of the booklet the real-world value of ADP concept is gifted, concentrating on 3 program examples constructed from the authors’ work:
• renewable strength scheduling for shrewdpermanent energy grids;• coal gasification tactics; and• water–gas shift reactions.
Researchers learning clever keep watch over 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 remedy of a complicated method of control.
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Additional info for Adaptive Dynamic Programming with Applications in Optimal Control
Dynamic programming is a very useful tool in solving optimization and optimal control problems. In particular, it can easily be applied to nonlinear systems with or without constraints on the control and state variables. 4) is called the functional equation of dynamic programming or Bellman equation and is the basis for computer implementation of dynamic programming. 2) are known, the solution for u∗ becomes a simple optimization problem. , as a result of the well-known “curse of dimensionality” [9, 23, 41].
7). In Figs. 3, xˆ k+1 is the output from the model network. 15), we can see that the learning objective is to minimize |rt+1 + γ V (st+1 ) − V (st )| by using rt+1 + γ V (st+1 ) as the learning target. This gives the same idea as in the forward-in-time approach shown in Fig. 2, where the target is Uk + γ Jˆk+1 . 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.
6) iteratively to provide approximate solutions. 3 Adaptive Dynamic Programming There are several schemes of dynamic programming [9, 11, 23, 41]. One can consider discrete-time systems or continuous-time systems, linear systems or nonlinear systems, time-invariant systems or time-varying systems, deterministic systems or stochastic systems, etc. Discrete-time (deterministic) nonlinear (time-invariant) dynamical systems will be discussed first. Time-invariant nonlinear systems cover most of the application areas and discrete-time is the basic consideration for digital implementation.