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Solution of Dynamic Optimization Problems by Successive Quadratic Programming and Orthogonal Collocation

IP.com Disclosure Number: IPCOM000148125D
Original Publication Date: 1983-Dec-14
Included in the Prior Art Database: 2007-Mar-29

Publishing Venue

Software Patent Institute

Related People

Biegler, Lorenz T.: AUTHOR [+2]

Abstract

Solution of Dynamic Optimization Problemp by Successive Quadratic Programming anp ,..O F.l.$ ;-,:: .: ;.:!,.:,,-q '. .... rt,hogonal Collocation \,.. .-, <.', ,; ..<,! ,;.,., ,, :..,I.",:, .!:: '-, . ,,\-. ..,.;. .~;r-, , ,, ?;::,;.d?K;.;;*-', . .. c:tC.[q r I Departmcnt of Chcrnical Engineering and I'hc Robotics Institute Carncgic-Mcllon University Pittsburgh, Pennsylvania 15213 14 Dcccmber 1983 Copyright 1983 Carncgic-Mcllon University I I Acknowlcdgcment is made to the Donors of the Pctrolcum Kcscarch Fund, adrninisdcred by the American Chemical Society, for partial support of this rcscarch. I i Table of Contents 1. Mcthod Development 2. Example 3. Cot~clusions 4. References List of Figu ues Figure 1: COMPARISON OF OPI'IMAI, PROFII,ES List of Tables 'Ihhlc 1: COMPAIIISON OF METHODSTable 2: OPTIMAL PROFILE A'1' COIIdOCATION POINTS Abstract Optimal control and cstimatjon problcms arc currently solved by cnlhcdding a dif rential cquation solver

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Solution of Dynamic Optimization Problemp by Successive Quadratic Programming anp

,..O

F.l.$ ;-,::

' .: ;.:!,.:,,-q '. !

....

rt,hogonal Collocation

\,.. .-, <.',

         ,; ..<,! ,;.,., ,, :..,I.",:,

.!:: '-, . ,,\-. ..,.;. .~;r-,

, ,,

?;::,;.d?K;.;;*-',

. .. c:tC.[q r I

Departmcnt of Chcrnical Engineering and I'hc Robotics Institute Carncgic-Mcllon University Pittsburgh, Pennsylvania 15213

14 Dcccmber 1983

Copyright @ 1983 Carncgic-Mcllon University I I

Acknowlcdgcment is made to the Donors of the Pctrolcum Kcscarch Fund, adrninisdcred by the American Chemical Society, for partial support of this rcscarch. \ I

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i

Table of Contents

1. Mcthod Development
2. Example

3. Cot~clusions
4. References

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List of Figu ues

Figure 1: COMPARISON OF OPI'IMAI, PROFII,ES

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                     List of Tables 'Ihhlc 1: COMPAIIISON OF METHODS
Table 2: OPTIMAL PROFILE A'1' COIIdOCATION POINTS

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Abstract

Optimal control and cstimatjon problcms arc currently solved by cnlhcdding a dif rential cquation solver

into thc optirnizatiotl strategy. The optimization algorithm chooscs thc co~lcrol profile, or parameter estimates, and rcquil-cs thc diffcrctltial cquation roiltinc to solve thc cquations and cv?luatc the objective and

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constraint functionals at each step. Two popular mcthods for optimal control that \follow this strategy are Control Vcctor Iteration (CVI) and Control Vcctor I'aramcterization (CVP). CVI cquires solution of the

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Eulcr-Lagrangc equations and mil~imizntion of the Harniltonian while CVP iilvolvb repeated dlffcrcniial equation solutions drivcn by dircct scarch optimization [I]. 1

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noth methods can bc prohibitively expensive cvcn for small problems bccauw they {cntl to convcrgc slowly l

and rcquire solution of differential cquations at each iteration. Wc introduce a rqethod that avoids this requirement by simultaneously converging to thc optimum whilc soivi:ig the diffcrcntiai cquations. To do

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this, we apply orthogoaal collocaticln ro the systc'm of diffcrcntial cquations and conv/crt then1 into atgcbraic oncs. We tllcn apply an optimizaiion stratcgy that does not rccluirc sziisfactioa of C ~ L I

lit;. constr~inls at tach

itcratio~l. Mcrc thc ~ncthod is applied to a :;...