Adaptive dynamic programming for control. Algorithms and stability
type: Item
instance of: scholarly article
title: Adaptive dynamic programming for control. Algorithms and stability
zbMATH Open document ID: 1279.49017
DOI: 10.1007/978-1-4471-4757-2
author: Huaguang Zhang
author: Derong Liu
author: Yanhong Luo
author: Ding Wang
published in: Communications and Control Engineering
publication date: 2012-12-13T00:00:00Z
review text: Adaptive Dynamic Programming (ADP) is a recursive method (algorithm) which aims to circumvent the classical computational and theoretical problems in solving the Hamilton-Jacobi-Bellman equation for an optimal control problem. This book is devoted to such a subject. From Chapter 1. ``A solution to the ADP formulation is obtained through a neural-network-based adaptive critic approach.'' ``Heuristic Dynamic Programming (HDP) is the most basic and widely applied structure of ADP. In HDP, the critic network will give an estimation of the cost function \(J\)''. ``In (the presented) HDP structure, there are two critic networks. During the ADP algorithm based on HDP, there are two iteration loops, i.e., an outer iteration loop and an inner iteration loop. The weights of the first critic network \(1\) are updated at each outer loop iteration step, and the weights of the second critic network are updated at each inner loop iteration step. During the inner loop iteration, the weights of the first critic network are kept unchanged. Once the whole inner loop iteration process is finished, the wights of the second critic network are transferred to the first critic network. The output of the second critic network is \(\hat J\), which is the estimate of \(J\).'' From the Preface. ``In the recent years, ADP algorithms have gained much attention from researchers in control fields. However, with the development of ADP algorithms, more and more people want to know the answers to the following questions: {\parindent=6mm \begin{itemize} \item[(1)] Are ADP algorithms convergent? \item [(2)] Can the algorithm stabilize a nonlinear plant? \item [(3)] Can the algorithm be run on-line? \item [(4)] Can the algorithm be implemented in a finite time horizon? \item [(5)] If the answer to the first question is positive, the subsequent questions are where the algorithm converges to, and how large the error is. \end{itemize}} Before ADP algorithms can be applied to real plants, these questions nee…
reviewed by: Fabio Bagagiolo
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 90C39
zbMATH DE Number: 6115350
zbMATH Keywords: adaptive dynamic programming
zbMATH Keywords: optimal control
zbMATH Keywords: Hamilton-Jacobi-Bellman equations
zbMATH Keywords: discrete-time
zbMATH Keywords: feedback controls
zbMATH Keywords: approximation
zbMATH Keywords: iterations
zbMATH Keywords: neural networks
zbMATH Keywords: nonlinear games
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4471-4757-2
OpenAlex ID: W2476930474
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description: scientific article; zbMATH DE number 6115350