optimal control summary - university of texas at arlington 05 neu short course/optimal control...
TRANSCRIPT
![Page 1: optimal control summary - University of Texas at Arlington 05 NEU short course/optimal control summary.pdf · Select design parameter weighting matrices Q = QT 2 0 R = RT > 0 Solve](https://reader033.vdocuments.us/reader033/viewer/2022041623/5e40a9acae48940d7464f9b0/html5/thumbnails/1.jpg)
Moncrief-O’Donnell Chair, UTA Research Institute (UTARI)The University of Texas at Arlington, USA
and
F.L. Lewis, NAI
Talk available online at http://www.UTA.edu/UTARI/acs
Summary of Optimal Control DesignSupported by :China Qian Ren Program, NEUChina Education Ministry Project 111 (No.B08015)NSF, ONR
Qian Ren Consulting Professor, State Key Laboratory of SyntheticalAutomation for Process Industries
Northeastern University, Shenyang, China
![Page 2: optimal control summary - University of Texas at Arlington 05 NEU short course/optimal control summary.pdf · Select design parameter weighting matrices Q = QT 2 0 R = RT > 0 Solve](https://reader033.vdocuments.us/reader033/viewer/2022041623/5e40a9acae48940d7464f9b0/html5/thumbnails/2.jpg)
![Page 3: optimal control summary - University of Texas at Arlington 05 NEU short course/optimal control summary.pdf · Select design parameter weighting matrices Q = QT 2 0 R = RT > 0 Solve](https://reader033.vdocuments.us/reader033/viewer/2022041623/5e40a9acae48940d7464f9b0/html5/thumbnails/3.jpg)
Static Optimization
min ( , )u
L x u
Subject to constraint ( , ) 0f x u
Solution. Define Hamiltonian function
( , , ) ( , ) ( . )TH x u L x u f x u
Adjoin constraints to the performance index using Lagrange multiplier
![Page 4: optimal control summary - University of Texas at Arlington 05 NEU short course/optimal control summary.pdf · Select design parameter weighting matrices Q = QT 2 0 R = RT > 0 Solve](https://reader033.vdocuments.us/reader033/viewer/2022041623/5e40a9acae48940d7464f9b0/html5/thumbnails/4.jpg)
Discrete-time Nonlinear Optimal Control
![Page 5: optimal control summary - University of Texas at Arlington 05 NEU short course/optimal control summary.pdf · Select design parameter weighting matrices Q = QT 2 0 R = RT > 0 Solve](https://reader033.vdocuments.us/reader033/viewer/2022041623/5e40a9acae48940d7464f9b0/html5/thumbnails/5.jpg)
![Page 6: optimal control summary - University of Texas at Arlington 05 NEU short course/optimal control summary.pdf · Select design parameter weighting matrices Q = QT 2 0 R = RT > 0 Solve](https://reader033.vdocuments.us/reader033/viewer/2022041623/5e40a9acae48940d7464f9b0/html5/thumbnails/6.jpg)
Steady-State Discrete-Time LQR
SOLUTION
![Page 7: optimal control summary - University of Texas at Arlington 05 NEU short course/optimal control summary.pdf · Select design parameter weighting matrices Q = QT 2 0 R = RT > 0 Solve](https://reader033.vdocuments.us/reader033/viewer/2022041623/5e40a9acae48940d7464f9b0/html5/thumbnails/7.jpg)
![Page 8: optimal control summary - University of Texas at Arlington 05 NEU short course/optimal control summary.pdf · Select design parameter weighting matrices Q = QT 2 0 R = RT > 0 Solve](https://reader033.vdocuments.us/reader033/viewer/2022041623/5e40a9acae48940d7464f9b0/html5/thumbnails/8.jpg)
![Page 9: optimal control summary - University of Texas at Arlington 05 NEU short course/optimal control summary.pdf · Select design parameter weighting matrices Q = QT 2 0 R = RT > 0 Solve](https://reader033.vdocuments.us/reader033/viewer/2022041623/5e40a9acae48940d7464f9b0/html5/thumbnails/9.jpg)
BuAxx u Kx
02
1 dtRuuQxxJ TT
Steady-State Continuous-Time LQR
System
Select input
To minimize the Performance Index
01 PBPBRQPAPA TT