Automatic solution of optimal-control problems. IV. Gradient method
type: Item
instance of: scholarly article
title: Automatic solution of optimal-control problems. IV. Gradient method
zbMATH Open document ID: 0554.65048
DOI: 10.1016/0096-3003(84)90026-2
published in: Applied Mathematics and Computation
publication date: 1984-01-01T00:00:00Z
review text: [For part I see ibid. 14, 131-148 (1984; reviewed above).] - The authors' table method for automatic calculations of derivatives of real functions of several variables is used to approximate by the gradient method the solution of the two point boundary value problem: \((x',p')=(H_ p(t,x,p,u),\quad -H_ x(t,x,p,u)),\) \(x(0)=x_ 0\), \(p(T)=0\), \(H_ u(t,x,p,u)=0\) associated by Pontryagin's maximum principle to the problem of minimizing \(\int^{T}_{0}F(t,x(t),u(t))dt\) subject to: \(x'(t)=f(t,x(t),u(t))\), \(x(0)=x_ 0\), x(t),u(t)\(\in R\); the Hamiltonian is defined as usual by: \(H(t,x,p,u)=F(t,x,u)+p.f(t,x,u).\) Numerical experiments for the problem defined by: \(F(t,x,u)=x^ 2+u^ 2\), \(f(t,x,u)=-ax-bx^ 2+u\), \(T=1\), \(x(0)=1\), in the cases: \((a,b)=(1,0.1)\), \((a,b)=(0,1)\) and \((a,b)=(0,0)\) are presented and an offer to provide on request the FORTRAN program listing is made.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 49M15
Mathematics Subject Classification ID: 49J15
zbMATH DE Number: 3883528
zbMATH Keywords: optimal control
zbMATH Keywords: gradient method
zbMATH Keywords: table method
zbMATH Keywords: automatic calculations of derivatives
zbMATH Keywords: Pontryagin's maximum principle
zbMATH Keywords: Numerical experiments
author: R. E. Kalaba
author: Karl Spingarn
reviewed by: Ştefan Mirică
MaRDI profile type: Publication
full work available at URL: 0096-3003(84)90026-2
OpenAlex ID: W2088363073
cites work: Q5580002
cites work: Control, identification, and input optimization
cites work: Q5587509
cites work: Automatic solution of optimal-control problems. I. Simplest problem in the calculus of variations
cites work: A simple automatic derivative evaluation program
cites work: Wengert's numerical method for partial derivatives, orbit determination and quasilinearization
description: scientific article; zbMATH DE number 3883528