Numerical solution of optimal control problems with explicit and implicit switches
In this article, we present a unified framework for the numerical solution of optimal control problems (OCPs) constrained by ordinary differential equations with both implicit and explicit switches. We present the problem class and qualify different types of implicitly switched systems. This classif...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
27 Mar 2018
|
| In: |
Optimization methods & software
Year: 2018, Volume: 33, Issue: 3, Pages: 450-474 |
| ISSN: | 1029-4937 |
| DOI: | 10.1080/10556788.2018.1449843 |
| Online Access: | Verlag, Volltext: https://doi.org/10.1080/10556788.2018.1449843
|
| Author Notes: | Hans Georg Bock, Christian Kirches, Andreas Meyer, Andreas Potschka |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1693434121 | ||
| 003 | DE-627 | ||
| 005 | 20220818022114.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 200327s2018 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1080/10556788.2018.1449843 |2 doi | |
| 035 | |a (DE-627)1693434121 | ||
| 035 | |a (DE-599)KXP1693434121 | ||
| 035 | |a (OCoLC)1341311530 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 28 |2 sdnb | ||
| 100 | 1 | |a Bock, Hans Georg |d 1948- |e VerfasserIn |0 (DE-588)1025289927 |0 (DE-627)721988717 |0 (DE-576)370169255 |4 aut | |
| 245 | 1 | 0 | |a Numerical solution of optimal control problems with explicit and implicit switches |c Hans Georg Bock, Christian Kirches, Andreas Meyer, Andreas Potschka |
| 264 | 1 | |c 27 Mar 2018 | |
| 300 | |a 25 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Gesehen am 27.03.2020 | ||
| 520 | |a In this article, we present a unified framework for the numerical solution of optimal control problems (OCPs) constrained by ordinary differential equations with both implicit and explicit switches. We present the problem class and qualify different types of implicitly switched systems. This classification significantly affects opportunities for solving such problems numerically. By using techniques from generalized disjunctive programming, we transform the problem into a counterpart one wherein discontinuities no longer appear implicitly. Instead, the new problem contains discrete decision variables and vanishing constraints. Recent results from the field of mixed-integer optimal control theory enable us to omit integrality constraints on variables, and allow to solve a relaxed OCP. We use a ‘first discretize, then optimize’ approach to solve the problem numerically. A direct method based on adaptive collocation is used for the discretization. The resulting finite dimensional optimization problems are mathematical programs with vanishing constraints, and we discuss numerical techniques to solve sequences of this challenging problem class. To demonstrate the efficacy and merit of our proposed approach, we investigate three benchmark problems for hybrid dynamic systems. | ||
| 650 | 4 | |a direct transcription methods | |
| 650 | 4 | |a generalized disjunctive programming | |
| 650 | 4 | |a mathematical programs with vanishing constraints | |
| 650 | 4 | |a mixed-integer optimal control | |
| 650 | 4 | |a optimal control | |
| 650 | 4 | |a switched systems | |
| 700 | 1 | |a Kirches, Christian |e VerfasserIn |0 (DE-588)143917161 |0 (DE-627)655909893 |0 (DE-576)339678429 |4 aut | |
| 700 | 1 | |a Meyer, Andreas |d 1986- |e VerfasserIn |0 (DE-588)1203667612 |0 (DE-627)1688693998 |4 aut | |
| 700 | 1 | |a Potschka, Andreas |d 1980- |e VerfasserIn |0 (DE-588)1019443391 |0 (DE-627)685041166 |0 (DE-576)358073995 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Optimization methods & software |d London [u.a.] : Taylor & Francis, 1992 |g 33(2018), 3, Seite 450-474 |h Online-Ressource |w (DE-627)266883532 |w (DE-600)1468203-5 |w (DE-576)259029246 |x 1029-4937 |7 nnas |a Numerical solution of optimal control problems with explicit and implicit switches |
| 773 | 1 | 8 | |g volume:33 |g year:2018 |g number:3 |g pages:450-474 |g extent:25 |a Numerical solution of optimal control problems with explicit and implicit switches |
| 856 | 4 | 0 | |u https://doi.org/10.1080/10556788.2018.1449843 |x Verlag |x Resolving-System |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20200327 | ||
| 993 | |a Article | ||
| 994 | |a 2018 | ||
| 998 | |g 1019443391 |a Potschka, Andreas |m 1019443391:Potschka, Andreas |d 700000 |d 708000 |d 110000 |e 700000PP1019443391 |e 708000PP1019443391 |e 110000PP1019443391 |k 0/700000/ |k 1/700000/708000/ |k 0/110000/ |p 4 |y j | ||
| 998 | |g 1203667612 |a Meyer, Andreas |m 1203667612:Meyer, Andreas |d 700000 |d 708000 |e 700000PM1203667612 |e 708000PM1203667612 |k 0/700000/ |k 1/700000/708000/ |p 3 | ||
| 998 | |g 143917161 |a Kirches, Christian |m 143917161:Kirches, Christian |p 2 | ||
| 998 | |g 1025289927 |a Bock, Hans Georg |m 1025289927:Bock, Hans Georg |d 700000 |d 708000 |e 700000PB1025289927 |e 708000PB1025289927 |k 0/700000/ |k 1/700000/708000/ |p 1 |x j | ||
| 999 | |a KXP-PPN1693434121 |e 3614756904 | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"type":{"bibl":"article-journal","media":"Online-Ressource"},"note":["Gesehen am 27.03.2020"],"recId":"1693434121","language":["eng"],"title":[{"title":"Numerical solution of optimal control problems with explicit and implicit switches","title_sort":"Numerical solution of optimal control problems with explicit and implicit switches"}],"person":[{"family":"Bock","given":"Hans Georg","roleDisplay":"VerfasserIn","display":"Bock, Hans Georg","role":"aut"},{"role":"aut","roleDisplay":"VerfasserIn","display":"Kirches, Christian","given":"Christian","family":"Kirches"},{"family":"Meyer","given":"Andreas","roleDisplay":"VerfasserIn","display":"Meyer, Andreas","role":"aut"},{"role":"aut","display":"Potschka, Andreas","roleDisplay":"VerfasserIn","given":"Andreas","family":"Potschka"}],"physDesc":[{"extent":"25 S."}],"relHost":[{"pubHistory":["1.1992 -"],"part":{"text":"33(2018), 3, Seite 450-474","volume":"33","extent":"25","year":"2018","issue":"3","pages":"450-474"},"physDesc":[{"extent":"Online-Ressource"}],"type":{"media":"Online-Ressource","bibl":"periodical"},"disp":"Numerical solution of optimal control problems with explicit and implicit switchesOptimization methods & software","language":["eng"],"recId":"266883532","origin":[{"publisher":"Taylor & Francis","dateIssuedKey":"1992","dateIssuedDisp":"1992-","publisherPlace":"London [u.a.]"}],"title":[{"title":"Optimization methods & software","title_sort":"Optimization methods & software"}],"id":{"issn":["1029-4937"],"zdb":["1468203-5"],"eki":["266883532"]}}],"origin":[{"dateIssuedDisp":"27 Mar 2018","dateIssuedKey":"2018"}],"id":{"doi":["10.1080/10556788.2018.1449843"],"eki":["1693434121"]},"name":{"displayForm":["Hans Georg Bock, Christian Kirches, Andreas Meyer, Andreas Potschka"]}} | ||
| SRT | |a BOCKHANSGENUMERICALS2720 | ||