Sequential quadratic programming methods for optimal control problems with state constraints
type: Item
instance of: scholarly article
title: Sequential quadratic programming methods for optimal control problems with state constraints
zbMATH Open document ID: 0807.49030
DOI: 10.1007/BF02662000
author: J. L. de Jong
author: Cheng-Xian Xu
published in: Applied Mathematics. Series B (English Edition)
publication date: 1995-02-16T00:00:00Z
review text: Some sequential quadratic programming methods for general optimal control problems with nonlinear dynamics, with fixed end time, with Bolza-type performance index, and with general boundary conditions on the initial and final states are proposed. It is assumed that all functions (including the controls) are of \(C^ 2\). After the repetition of the first and second order necessary and second order sufficient conditions of optimality, the quadratic approximation of the performance index and the linear approximation of the state equation and boundary condition in a neighbourhood of the optimal solution is constructed. This way (combined with the penalty function method) a linear-quadratic optimal control problem is obtained, which is next treated as a quadratic programming problem in a Banach space. Using the optimality conditions, a linear multipoint boundary value problem is constructed, the solution of which gives us the correction for the control and for the trajectory. Next, the discrete (i.e., finite-dimensional) sequential quadratic programming method is proposed after the discretization of the time, state equation, and performance index. The augmented Lagrangian with a penalty term is constructed and the corresponding iterative procedure is presented. There aren't any examples and comparison with other methods.
reviewed by: Z.Wyderka
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 49M29
Mathematics Subject Classification ID: 49M05
Mathematics Subject Classification ID: 49N10
zbMATH DE Number: 549488
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: merit function
zbMATH Keywords: sequential quadratic programming methods
zbMATH Keywords: performance index
zbMATH Keywords: multipoint boundary value problem
MaRDI profile type: Publication
cites work: Q3690580
cites work: OPTIMAL PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS
cites work: Q3928936
cites work: A proof of the convergence of the Kelley-Bryson penalty function technique for state-constrained control problems
cites work: Nonlinear programming applied to state-constrained optimization problems
cites work: Q3811611
full work available at URL: https://doi.org/10.1007/bf02662000
OpenAlex ID: W91349700
description: scientific article; zbMATH DE number 549488