IEICE TRANSACTIONS on Fundamentals
Moment Vector Equation for Nonlinear Systems and Its Application to Optimal Control
Summary :
A method was developed for deriving the control input for a multi-dimensional discrete-time nonlinear system so that a performance index is approximately minimized. First, a moment vector equation (MVE) is derived; it is a multi-dimensional linear equation that approximates a nonlinear system in the whole domain of the system state and control input. Next, the performance index is approximated by using a quadratic form with respect to the moment vector. On the basis of the MVE and the quadratic form, an approximate optimal controller is derived by solving the linear quadratic optimal control problem. A bilinear optimal control problem and a mountain-car problem were solved using this method, and the solutions were nearly optimal.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.10 pp.2522-2530
- Publication Date
- 2009/10/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E92.A.2522
- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
- Category
- Nonlinear Problems
Authors
Keyword
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Hideki SATOH, "Moment Vector Equation for Nonlinear Systems and Its Application to Optimal Control" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 10, pp. 2522-2530, October 2009, doi: 10.1587/transfun.E92.A.2522.
Abstract: A method was developed for deriving the control input for a multi-dimensional discrete-time nonlinear system so that a performance index is approximately minimized. First, a moment vector equation (MVE) is derived; it is a multi-dimensional linear equation that approximates a nonlinear system in the whole domain of the system state and control input. Next, the performance index is approximated by using a quadratic form with respect to the moment vector. On the basis of the MVE and the quadratic form, an approximate optimal controller is derived by solving the linear quadratic optimal control problem. A bilinear optimal control problem and a mountain-car problem were solved using this method, and the solutions were nearly optimal.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.2522/_p
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@ARTICLE{e92-a_10_2522,
author={Hideki SATOH, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Moment Vector Equation for Nonlinear Systems and Its Application to Optimal Control},
year={2009},
volume={E92-A},
number={10},
pages={2522-2530},
abstract={A method was developed for deriving the control input for a multi-dimensional discrete-time nonlinear system so that a performance index is approximately minimized. First, a moment vector equation (MVE) is derived; it is a multi-dimensional linear equation that approximates a nonlinear system in the whole domain of the system state and control input. Next, the performance index is approximated by using a quadratic form with respect to the moment vector. On the basis of the MVE and the quadratic form, an approximate optimal controller is derived by solving the linear quadratic optimal control problem. A bilinear optimal control problem and a mountain-car problem were solved using this method, and the solutions were nearly optimal.},
keywords={},
doi={10.1587/transfun.E92.A.2522},
ISSN={1745-1337},
month={October},}
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TY - JOUR
TI - Moment Vector Equation for Nonlinear Systems and Its Application to Optimal Control
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2522
EP - 2530
AU - Hideki SATOH
PY - 2009
DO - 10.1587/transfun.E92.A.2522
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2009
AB - A method was developed for deriving the control input for a multi-dimensional discrete-time nonlinear system so that a performance index is approximately minimized. First, a moment vector equation (MVE) is derived; it is a multi-dimensional linear equation that approximates a nonlinear system in the whole domain of the system state and control input. Next, the performance index is approximated by using a quadratic form with respect to the moment vector. On the basis of the MVE and the quadratic form, an approximate optimal controller is derived by solving the linear quadratic optimal control problem. A bilinear optimal control problem and a mountain-car problem were solved using this method, and the solutions were nearly optimal.
ER -
English
