Finite-time optimal control of polynomial systems using successive suboptimal approximations
type: Item
instance of: scholarly article
title: Finite-time optimal control of polynomial systems using successive suboptimal approximations
zbMATH Open document ID: 0980.49028
DOI: 10.1023/A:1004674221393
author: R. Smith
published in: Journal of Optimization Theory and Applications
publication date: 2001-05-09T00:00:00Z
review text: The paper is focused on the problem of time-optimal control of polynomial systems. It shows that this optimalization problem may be solved on the way of creation of a sequence of optimal control problems for the linear problem. The subject of the paper is the controlled object \[ \dot{x}=p(x,u,t) \] where \(x \in R^{n}, u \in R^{m}\). The problem deals with a quadratic criterion of optimality. As problem solution it has been presented an iterative procedure. The proposed method consists of the following steps: i. Quasi-linearization of the polynomial system at the step \(k \rightarrow 1\) around of the solution of iteration \(k\). ii. Solution of the optimal control problem. A proof of the convergence is presented, i.e., the iteration converges if the weight \(R\) on the control inputs is large. Numerical examples interpret the idea of problem solution.
reviewed by: Władysław Hejmo
Mathematics Subject Classification ID: 49N10
Mathematics Subject Classification ID: 49M30
Mathematics Subject Classification ID: 93B40
zbMATH DE Number: 1523638
zbMATH Keywords: optimal control
zbMATH Keywords: linearization of non-linear problem
zbMATH Keywords: approximation
MaRDI profile type: Publication
cites work: An iterative method for the finite-time bilinear-quadratic control problem
cites work: The successive approximation procedure for finite-time optimal control of bilinear systems
cites work: Construction of optimal feedback control for nonlinear systems via Chebyshev polynomials
cites work: Q4857368
cites work: On Global Representations of the Solutions of Linear Differential Equations as a Product of Exponentials
full work available at URL: a:1004674221393
OpenAlex ID: W157651561
description: scientific article; zbMATH DE number 1523638