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Kendali Optimal
(EL6221)
Bambang Riyanto
7/21/2019 Kendali_Optimal.pptx
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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"
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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 $ocus on bot! t!e tec!ni0ue7approac!and t!e control result
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5re8re0uistes
• Course assumes a good 9or4ing 4no9ledge o$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"
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e't Boo4
• Optimal Control. Linear uadratic,et!ods" e9 =or4& =. Do%er& 2>>?"#;B. @?A>A6?666& B"D"O"
-nderson and " ,oore
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Course E%aluation
• -ssignment . 2>
• 5roect . F>
•
Ginal e'am . >
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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)"
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D-R5- 3rand C!allenge
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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"
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Gounding Gat!ers
Lev Pontryagin
(Rusia, 1!"-1""#
$aximum Principle
Richard %ellman
(&, 1)!-1"*#
+ynamic Programming
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;o$t9are
• ,atlab • ;cilab