Feedback control method using Haar wavelet operational matrices for solving optimal control problems
type: Item
instance of: scholarly article
title: Feedback control method using Haar wavelet operational matrices for solving optimal control problems
zbMATH Open document ID: 1291.93253
DOI: 10.1155/2013/240352
author: Waleeda Swaidan
author: Amran Hussin
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: Most of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical technique, which is based on the combination of Haar wavelet collocation method and successive Generalized Hamilton-Jacobi-Bellman equation. We formulate some new Haar wavelet operational matrices in order to manipulate Haar wavelet series. The proposed method has been applied to solve linear and nonlinear optimal control problems with infinite time horizon. The simulation results indicate that the accuracy of the control and cost can be improved by increasing the wavelet resolution.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 49N35
zbMATH DE Number: 6306552
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/240352
OpenAlex ID: W2058756797
Wikidata QID: Q58915627
cites work: Successive Galerkin approximation algorithms for nonlinear optimal and robust control
cites work: A game theoretic algorithm to compute local stabilizing solutions to HJBI equations in nonlinear \(H_\infty \) control
cites work: Numerical approach to computing nonlinear H-infinity control laws
cites work: An approach for solving the Hamilton-Jacobi-Isaacs equation (HJIE) in nonlinear \(\mathcal H_{\infty}\) control
cites work: Policy Iterations on the Hamilton–Jacobi–Isaacs Equation for $H_{\infty}$ State Feedback Control With Input Saturation
cites work: Robustness of nonlinear state feedback. A survey
cites work: Direct and indirect methods for trajectory optimization
cites work: Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation
cites work: Feedback control methodologies for nonlinear systems
cites work: Haar wavelet method for solving lumped and distributed-parameter systems
cites work: Optimal control of linear time-varying systems via Haar wavelets
cites work: Wavelet collocation method for optimal control problems
cites work: Numerical solution of time-varying functional differential equations via Haar wavelets
cites work: Kronecker products and matrix calculus in system theory
cites work: Q4003793
cites work: Q3200939
description: scientific article; zbMATH DE number 6306552