Numerical methods for optimal control problems with state constraints
type: Item
instance of: scholarly article
title: Numerical methods for optimal control problems with state constraints
zbMATH Open document ID: 0928.49002
published in: Lecture Notes in Mathematics
publication date: 1999-09-22T00:00:00Z
review text: The author considers optimal control problems with pathwise state inequality constraints of the form \[ \min_u\Phi(x(1)), \] \[ x'(t)= f(t,x(t),u(t))\;\forall t\in [0,1],\;x(0)= x_0, \] \[ u(t)\in \Omega,\quad h^1_i(x(1))= 0,\quad h^2_j(x(1))\leq 0. \] For this problems, first- and second-order solution methods are discussed. The book has the following chapters: 1. Introduction, 2. Estimates on solutions to differential equations and their approximations, 3. First order method, 4. Implementation, 5. Second-order method, 6. Runge-Kutta based procedure for optimal control of differential-algebraic equations. In the Appendix A, a primal range-space method for piecewise-linear quadratic programming is given. The author gives also remarks on numerical software developed in connection with the derived methods.
Mathematics Subject Classification ID: 49-02
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 49M99
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 1342607
zbMATH Keywords: numerical methods
zbMATH Keywords: optimal control problems
zbMATH Keywords: pathwise state inequality constraints
author: Radosław Pytlak
reviewed by: Hans Benker
describes a project that uses: CFSQP
describes a project that uses: GAMS
describes a project that uses: CONOPT
describes a project that uses: ODEPACK
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0097244
OpenAlex ID: W1551493992
DOI: 10.1007/BFB0097244
description: scientific article; zbMATH DE number 1342607