Kendali_Optimal.pptx

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 1/14

Kendali Optimal

(EL6221)

Bambang Riyanto

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 2/14

Course Description

  !is course studies basic optimization andthe principles of optimal control" #tconsiders deterministic and stochastic 

problems $or bot! discrete-time andcontinuous-time systems" !e course co%erssolution met!ods including numerical searc!algorit!ms& model predicti%e control& dynamicprogramming& variational calculus& andapproac!es based on Pontryagin'smaximum principle& and it includes manye'amples and applications o$ t!e t!eory"

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 3/14

Obecti%es

• onlinear optimi*ation + ,-L-Bimplementation

• Dynamic Optimi*ation approac!es. dynamic

programming& Calculus o$ /ariations• Linear 0uadratic regulator (LR)& Kalman

lter& Linear uadratic 3aussian (L3)

• #n%estigate 4ey basic control concepts and

e'tend to ad%anced algorit!ms (,5C)

• ill $ocus on bot! t!e tec!ni0ue7approac!and t!e control result

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 4/14

5re8re0uistes

• Course assumes a good 9or4ing 4no9ledge o$linear algebra and di:erential e0uations" e9material 9ill be co%ered in dept! in t!e class&

but a strong bac4ground 9ill be necessary"• ;olid bac4ground in control design (classical

control < multi%ariable7state space control) isbest to $ully understand t!is material& but not

essential"• Course material and !ome9or4 assume a

good 9or4ing 4no9ledge o$ ,-L-B"

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 5/14

 e't Boo4

• Optimal Control. Linear uadratic,et!ods" e9 =or4& =. Do%er& 2>>?"#;B. @?A>A6?666& B"D"O"

-nderson and " ,oore

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 6/14

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 7/14

Course E%aluation

• -ssignment . 2>

• 5roect . F>

•

Ginal e'am . >

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 8/14

Optimal Control

• Optimal control deals 9it! t!e problem o$ nding acontrol la9 $or a gi%en system suc! t!at a certainoptimality criterion is ac!ie%ed"

• - control problem includes a cost $unctional t!at is a

$unction o$ state and control %ariables"• -n optimal control is a set o$ di:erential e0uations

describing t!e pat!s o$ t!e control %ariables t!atminimi*e t!e cost $unctional"

• !e optimal control can be deri%ed using5ontryaginHs ma'imum principle (a necessarycondition)& or by sol%ing t!e Iamilton8acobi8Bellmane0uation (a suJcient condition)"

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 9/14

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 10/14

D-R5- 3rand C!allenge

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 11/14

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 12/14

E'ample

• -not!er optimal control problem is tond t!e 9ay to dri%e t!e car so as tominimi*e its $uel consumption& gi%en

t!at it must complete a gi%en coursein a time not e'ceeding some amount"

•  =et anot!er control problem is to

minimi*e t!e total monetary cost o$completing t!e trip& gi%en assumedmonetary prices $or time and $uel"

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 13/14

Gounding Gat!ers

Lev Pontryagin

(Rusia, 1!"-1""#

$aximum Principle

Richard %ellman

(&, 1)!-1"*#

+ynamic Programming

7/21/2019 Kendali_Optimal.pptx

http://slidepdf.com/reader/full/kendalioptimalpptx 14/14

;o$t9are

• ,atlab   • ;cilab