A numerical method for hybrid optimal control based on dynamic programming
This contribution extends a numerical method for solving optimal control problems by dynamic programming to a class of hybrid dynamic systems with autonomous as well as controlled switching. The value function of the hybrid control system is calculated based on a full discretization of the state and...
Saved in:
| Published in: | Nonlinear analysis. Hybrid systems Vol. 5; no. 2; pp. 254 - 274 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Ltd
01.05.2011
|
| Subjects: | |
| ISSN: | 1751-570X |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | This contribution extends a numerical method for solving optimal control problems by dynamic programming to a class of hybrid dynamic systems with autonomous as well as controlled switching. The value function of the hybrid control system is calculated based on a full discretization of the state and input spaces. A bound for the error due to discretization is obtained from modeling the error as perturbation of the continuous dynamics and the cost terms. It is shown that the bound approaches zero and that the value function of the discretized variant converges to the value function of the original problem if the discretization parameters go to zero. The performance of a numerical scheme exploiting the discretized system is illustrated for two different examples treated previously in literature. |
|---|---|
| AbstractList | This contribution extends a numerical method for solving optimal control problems by dynamic programming to a class of hybrid dynamic systems with autonomous as well as controlled switching. The value function of the hybrid control system is calculated based on a full discretization of the state and input spaces. A bound for the error due to discretization is obtained from modeling the error as perturbation of the continuous dynamics and the cost terms. It is shown that the bound approaches zero and that the value function of the discretized variant converges to the value function of the original problem if the discretization parameters go to zero. The performance of a numerical scheme exploiting the discretized system is illustrated for two different examples treated previously in literature. |
| Author | Stursberg, Olaf Rungger, Matthias |
| Author_xml | – sequence: 1 givenname: Matthias surname: Rungger fullname: Rungger, Matthias email: matthias.rungger@uni-kassel.de – sequence: 2 givenname: Olaf surname: Stursberg fullname: Stursberg, Olaf email: stursberg@uni-kassel.de |
| BookMark | eNp9kD1rwzAQhjWk0KTtH-jkrZPds2TFMnQJoZ8EurTQTUjyOVGwpVRyCvn3VUinDpkO7t7njntmZOK8Q0JuSyhKKOf328KpTSwopAY0BQCdkGlZ8zLnNXxdklmMWwDeUFFNydsic_sBgzWqzwYcN77NOh-yzUEH22Z-N9ohTYx3Y_B9plXE1HVZe3BqsCbbBb8OahisW1-Ti071EW_-6hX5fHr8WL7kq_fn1-VilRvG6JgLRruWM6S8ZUzwrtNadFzXuuY1VnNRsbbWFEBzOtdzpqDCDgUXlWpAsArZFbk77U23v_cYRznYaLDvlUO_j1LUHJoSWJ2S9JQ0wccYsJO7kN4JB1mCPLqSW3l0JY-uJDQyuUqQ-AcZO6rRHg0o259HH04opvd_LAYZjUVnsLUBzShbb8_hvxR3iWg |
| CitedBy_id | crossref_primary_10_1109_TFUZZ_2023_3348535 crossref_primary_10_1016_j_automatica_2016_11_040 crossref_primary_10_1155_2012_457121 crossref_primary_10_23919_JSEE_2022_000114 crossref_primary_10_1109_TNNLS_2013_2288067 crossref_primary_10_1515_auto_2018_0080 crossref_primary_10_1109_TNNLS_2015_2388672 crossref_primary_10_3390_pr8020170 crossref_primary_10_1016_j_asoc_2016_09_007 |
| Cites_doi | 10.1109/9.654885 10.1109/CDC.2009.5400068 10.1109/9.847100 10.1109/9.273337 10.1023/A:1017992615625 10.1109/CDC.1999.827981 10.1109/TAC.2007.904451 10.1007/BF01448394 10.1109/CDC.2010.5718054 10.1007/s00211-004-0555-4 10.1007/BF01442644 10.1137/040618072 10.1109/CDC.1999.832814 10.3182/20090916-3-ES-3003.00055 10.1007/s002110050241 10.1109/CDC.1999.831404 10.1109/CDC.2004.1430241 10.3182/20090916-3-ES-3003.00053 10.1109/CDC.1995.478514 10.1109/TAC.2009.2015528 10.1049/ip-cta:20050094 10.1109/MCS.2008.931718 10.1016/S1474-6670(17)36459-5 |
| ContentType | Journal Article |
| Copyright | 2010 Elsevier Ltd |
| Copyright_xml | – notice: 2010 Elsevier Ltd |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| DOI | 10.1016/j.nahs.2010.09.002 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EndPage | 274 |
| ExternalDocumentID | 10_1016_j_nahs_2010_09_002 S1751570X10000683 |
| GroupedDBID | --K --M .~1 0R~ 123 1B1 1~. 1~5 4.4 457 4G. 5VS 7-5 71M 8P~ AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAXUO ABAOU ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFS ACNNM ACRLP ADBBV ADEZE ADMUD ADTZH AEBSH AECPX AEKER AFKWA AFTJW AGHFR AGUBO AGYEJ AHJVU AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR AXJTR BJAXD BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FIRID FNPLU FYGXN GBLVA HZ~ IHE J1W J9A JJJVA KOM M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 RIG ROL RPZ SDF SDG SES SPC SPCBC SPD SST SSW SSZ T5K ~G- 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| ID | FETCH-LOGICAL-c332t-832fd53e25d3385ffbb8f5b7b757e46843d7b200b526b63a04efe8584a90834e3 |
| ISICitedReferencesCount | 21 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000302581600012&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1751-570X |
| IngestDate | Sat Sep 27 19:22:13 EDT 2025 Sat Nov 29 07:04:27 EST 2025 Tue Nov 18 22:41:13 EST 2025 Fri Feb 23 02:29:09 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Hybrid systems Value function Approximation Dynamic programming Optimal control |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c332t-832fd53e25d3385ffbb8f5b7b757e46843d7b200b526b63a04efe8584a90834e3 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 875091037 |
| PQPubID | 23500 |
| PageCount | 21 |
| ParticipantIDs | proquest_miscellaneous_875091037 crossref_primary_10_1016_j_nahs_2010_09_002 crossref_citationtrail_10_1016_j_nahs_2010_09_002 elsevier_sciencedirect_doi_10_1016_j_nahs_2010_09_002 |
| PublicationCentury | 2000 |
| PublicationDate | 2011-05-01 |
| PublicationDateYYYYMMDD | 2011-05-01 |
| PublicationDate_xml | – month: 05 year: 2011 text: 2011-05-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationTitle | Nonlinear analysis. Hybrid systems |
| PublicationYear | 2011 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | Caines, Shaikh (br000070) 2006 Goebel, Sanfelice, Teel (br000010) 2009; 29 R.L.V. González, M.M. Tidball, On the rates of convergence of fully discrete solutions of Hamilton–Jacobi equations. Technical Report 1376, Institut National de Recherche en Informatique et en Automatique, INRIA, 1991. Grüne (br000150) 2004; 99 Dharmatti, Ramaswamy (br000035) 2005; 44 Branicky, Borkar, Mitter (br000030) 1998; 43 A. Bemporad, D. Corona, A. Giua, C. Seatzu, Optimal state-feedback quadratic regulation of linear hybrid automata, in: IFAC Conf. on Analysis and Design of Hybrid Systems, 2003, pp. 407–412. R.L.V. González, M.M. Tidball, On a discrete time approximation of the Hamilton–Jacobi equation of dynamic programming. Technical Report 1375, Institut National de Recherche en Informatique et en Automatique, INRIA, 1991. S. Hedlund, A. Rantzer, Optimal control of hybrid systems, in: Conference on Decision and Control, 1999, pp. 3972–3977. Grüne (br000090) 1997; 75 Rantzer, Johansson (br000040) 2000; 45 B. Passenberg, O. Stursberg, A graph search algorithm for optimizing the discrete location sequence in hybrid optimal control problems, in: IFAC Conf. on Analysis and Design of Hybrid Systems, 2009, pp. 304–309. Munos, Moore (br000095) 2001; 49 H.J. Sussmann, A maximum principle for hybrid optimal control problems, in: Conference on Decision and Control, 1999, pp. 425–430. M. Rungger, O. Stursberg, Optimal control of deterministic hybrid systems using dynamic programming, in: IFAC Conf. on Analysis and Design of Hybrid Systems, 2009, pp. 316–321. Davies (br000160) 1997; 9 Capuzzo Dolcetta (br000120) 1983; 10 Kushner, Dupuis (br000100) 1992 Bertsekas (br000005) 1995 O. Stursberg, A graph search algorithm for optimal control of hybrid systems, in: Conference on Decision and Control, 2004, pp. 1412–1417. X. Xu, P.J. Antsaklis, Optimal control of switched autonomous systems, in: Conference on Decision and Control, 2002, pp. 4401–4406. M.S. Branicky, S.K. Mitter, Algorithms for optimal hybrid control, in: Conference on Decision and Control, 1995, pp. 2661–2666. Bengea, DeCarlo (br000085) 2005; 41 Kreisselmeier, Birkhölzer (br000115) 1994; 39 Falcone (br000125) 1987; 15 D.W. Moore, Simplicial mesh generation with applications, Ph.D. Thesis, Cornell University, 1992. Khalil (br000145) 1992 M. Rungger, O. Stursberg, Function approximation for the deterministic Hamilton–Jacobi–Bellman equation, in: IEEE Conference on Decision and Control, 2009, pp. 2268–2273. Bardi, Capuzzo-Dolcetta (br000105) 1997 M. Rungger, O. Stursberg, Continuity of the value function for exit time optimal control problems of hybrid systems, in: IEEE Conference on Decision and Control, 2010 (in press). P. Riedinger, F. Kratz, C. Iung, C. Zanne, Linear quadratic optimization for hybrid systems, in: Conference on Decision and Control, 1999, pp. 3059–3064. Shaikh, Caines, Shaikh, Caines (br000025) 2007; 52 Rantzer (br000045) 2006; 153 Davies (10.1016/j.nahs.2010.09.002_br000160) 1997; 9 Rantzer (10.1016/j.nahs.2010.09.002_br000040) 2000; 45 10.1016/j.nahs.2010.09.002_br000015 10.1016/j.nahs.2010.09.002_br000135 10.1016/j.nahs.2010.09.002_br000155 10.1016/j.nahs.2010.09.002_br000055 10.1016/j.nahs.2010.09.002_br000110 10.1016/j.nahs.2010.09.002_br000020 Branicky (10.1016/j.nahs.2010.09.002_br000030) 1998; 43 10.1016/j.nahs.2010.09.002_br000140 10.1016/j.nahs.2010.09.002_br000060 Kushner (10.1016/j.nahs.2010.09.002_br000100) 1992 10.1016/j.nahs.2010.09.002_br000080 Grüne (10.1016/j.nahs.2010.09.002_br000090) 1997; 75 Grüne (10.1016/j.nahs.2010.09.002_br000150) 2004; 99 Bengea (10.1016/j.nahs.2010.09.002_br000085) 2005; 41 Rantzer (10.1016/j.nahs.2010.09.002_br000045) 2006; 153 Kreisselmeier (10.1016/j.nahs.2010.09.002_br000115) 1994; 39 Caines (10.1016/j.nahs.2010.09.002_br000070) 2006 Falcone (10.1016/j.nahs.2010.09.002_br000125) 1987; 15 Shaikh (10.1016/j.nahs.2010.09.002_br000025_1) 2007; 52 Shaikh (10.1016/j.nahs.2010.09.002_br000025_2) 2009; 54 10.1016/j.nahs.2010.09.002_br000165 Bertsekas (10.1016/j.nahs.2010.09.002_br000005) 1995 10.1016/j.nahs.2010.09.002_br000065 10.1016/j.nahs.2010.09.002_br000075 10.1016/j.nahs.2010.09.002_br000130 Goebel (10.1016/j.nahs.2010.09.002_br000010) 2009; 29 10.1016/j.nahs.2010.09.002_br000050 Munos (10.1016/j.nahs.2010.09.002_br000095) 2001; 49 Khalil (10.1016/j.nahs.2010.09.002_br000145) 1992 Dharmatti (10.1016/j.nahs.2010.09.002_br000035) 2005; 44 Bardi (10.1016/j.nahs.2010.09.002_br000105) 1997 Capuzzo Dolcetta (10.1016/j.nahs.2010.09.002_br000120) 1983; 10 |
| References_xml | – reference: M.S. Branicky, S.K. Mitter, Algorithms for optimal hybrid control, in: Conference on Decision and Control, 1995, pp. 2661–2666. – volume: 44 start-page: 1259 year: 2005 end-page: 1288 ident: br000035 article-title: Hybrid control systems and viscosity solutions publication-title: SIAM Journal on Control and Optimization – volume: 75 start-page: 319 year: 1997 end-page: 337 ident: br000090 article-title: An adaptive grid scheme for the discrete Hamilton–Jacobi–Bellman equation publication-title: Numerische Mathematik – reference: M. Rungger, O. Stursberg, Function approximation for the deterministic Hamilton–Jacobi–Bellman equation, in: IEEE Conference on Decision and Control, 2009, pp. 2268–2273. – reference: R.L.V. González, M.M. Tidball, On a discrete time approximation of the Hamilton–Jacobi equation of dynamic programming. Technical Report 1375, Institut National de Recherche en Informatique et en Automatique, INRIA, 1991. – reference: H.J. Sussmann, A maximum principle for hybrid optimal control problems, in: Conference on Decision and Control, 1999, pp. 425–430. – volume: 43 start-page: 31 year: 1998 end-page: 45 ident: br000030 article-title: A unified framework for hybrid control: model and optimal control theory publication-title: IEEE Transactions on Automatic Control – year: 1997 ident: br000105 article-title: Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations – volume: 45 start-page: 629 year: 2000 end-page: 637 ident: br000040 article-title: Piecewise linear quadratic optimal control publication-title: IEEE Transactions on Automatic Control – reference: O. Stursberg, A graph search algorithm for optimal control of hybrid systems, in: Conference on Decision and Control, 2004, pp. 1412–1417. – volume: 52 start-page: 1587 year: 2007 end-page: 1603 ident: br000025 article-title: On the hybrid optimal control problem: theory and algorithms publication-title: IEEE Transactions on Automatic Control – reference: A. Bemporad, D. Corona, A. Giua, C. Seatzu, Optimal state-feedback quadratic regulation of linear hybrid automata, in: IFAC Conf. on Analysis and Design of Hybrid Systems, 2003, pp. 407–412. – volume: 41 start-page: 11 year: 2005 end-page: 27 ident: br000085 article-title: Optimal control of switching systems publication-title: Automatica – volume: 29 start-page: 28 year: 2009 end-page: 93 ident: br000010 article-title: Hybrid dynamical systems publication-title: IEEE Control Systems Magazine – volume: 10 start-page: 367 year: 1983 end-page: 388 ident: br000120 article-title: On a discrete approximation of the Hamilton–Jacobi equation of dynamic programming publication-title: Applied Mathematics and Optimization – reference: X. Xu, P.J. Antsaklis, Optimal control of switched autonomous systems, in: Conference on Decision and Control, 2002, pp. 4401–4406. – year: 1992 ident: br000100 article-title: Numerical Methods for Stochastic Control Problems in Continuous Time – volume: 39 start-page: 33 year: 1994 end-page: 46 ident: br000115 article-title: Numerical nonlinear regulator design publication-title: IEEE Transactions on Automatic Control – reference: M. Rungger, O. Stursberg, Continuity of the value function for exit time optimal control problems of hybrid systems, in: IEEE Conference on Decision and Control, 2010 (in press). – volume: 49 start-page: 291 year: 2001 end-page: 323 ident: br000095 article-title: Variable resolution discretization in optimal control publication-title: Machine Learning Journal – year: 1995 ident: br000005 article-title: Dynamic Programming and Optimal Control – reference: S. Hedlund, A. Rantzer, Optimal control of hybrid systems, in: Conference on Decision and Control, 1999, pp. 3972–3977. – reference: M. Rungger, O. Stursberg, Optimal control of deterministic hybrid systems using dynamic programming, in: IFAC Conf. on Analysis and Design of Hybrid Systems, 2009, pp. 316–321. – year: 1992 ident: br000145 article-title: Nonlinear Systems – start-page: 123 year: 2006 end-page: 137 ident: br000070 article-title: Optimality zone algorithms for hybrid systems: efficient algorithms for optimal location and control computation publication-title: Hybrid Systems: Computation and Control – reference: R.L.V. González, M.M. Tidball, On the rates of convergence of fully discrete solutions of Hamilton–Jacobi equations. Technical Report 1376, Institut National de Recherche en Informatique et en Automatique, INRIA, 1991. – reference: P. Riedinger, F. Kratz, C. Iung, C. Zanne, Linear quadratic optimization for hybrid systems, in: Conference on Decision and Control, 1999, pp. 3059–3064. – reference: B. Passenberg, O. Stursberg, A graph search algorithm for optimizing the discrete location sequence in hybrid optimal control problems, in: IFAC Conf. on Analysis and Design of Hybrid Systems, 2009, pp. 304–309. – reference: D.W. Moore, Simplicial mesh generation with applications, Ph.D. Thesis, Cornell University, 1992. – volume: 99 start-page: 85 year: 2004 end-page: 112 ident: br000150 article-title: Error estimation and adaptive discretization for the discrete stochastic Hamilton–Jacobi–Bellman equation publication-title: Numerische Mathematik – volume: 9 year: 1997 ident: br000160 article-title: Multidimensional triangulation and interpolation for reinforcement learning publication-title: Neural Information Processing Systems – volume: 153 start-page: 567 year: 2006 end-page: 574 ident: br000045 article-title: Relaxed dynamic programming in switching systems publication-title: IEE Proceedings — Control Theory & Applications – volume: 15 start-page: 1 year: 1987 end-page: 13 ident: br000125 article-title: A numerical approach to the infinite horizon problem of deterministic control theory publication-title: Applied Mathematics and Optimization – ident: 10.1016/j.nahs.2010.09.002_br000155 – ident: 10.1016/j.nahs.2010.09.002_br000130 – volume: 43 start-page: 31 issue: 1 year: 1998 ident: 10.1016/j.nahs.2010.09.002_br000030 article-title: A unified framework for hybrid control: model and optimal control theory publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.654885 – ident: 10.1016/j.nahs.2010.09.002_br000165 doi: 10.1109/CDC.2009.5400068 – volume: 45 start-page: 629 issue: 4 year: 2000 ident: 10.1016/j.nahs.2010.09.002_br000040 article-title: Piecewise linear quadratic optimal control publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.847100 – year: 1997 ident: 10.1016/j.nahs.2010.09.002_br000105 – volume: 39 start-page: 33 year: 1994 ident: 10.1016/j.nahs.2010.09.002_br000115 article-title: Numerical nonlinear regulator design publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.273337 – volume: 49 start-page: 291 year: 2001 ident: 10.1016/j.nahs.2010.09.002_br000095 article-title: Variable resolution discretization in optimal control publication-title: Machine Learning Journal doi: 10.1023/A:1017992615625 – volume: 9 year: 1997 ident: 10.1016/j.nahs.2010.09.002_br000160 article-title: Multidimensional triangulation and interpolation for reinforcement learning publication-title: Neural Information Processing Systems – ident: 10.1016/j.nahs.2010.09.002_br000065 doi: 10.1109/CDC.1999.827981 – volume: 52 start-page: 1587 year: 2007 ident: 10.1016/j.nahs.2010.09.002_br000025_1 article-title: On the hybrid optimal control problem: theory and algorithms publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2007.904451 – year: 1995 ident: 10.1016/j.nahs.2010.09.002_br000005 – volume: 10 start-page: 367 year: 1983 ident: 10.1016/j.nahs.2010.09.002_br000120 article-title: On a discrete approximation of the Hamilton–Jacobi equation of dynamic programming publication-title: Applied Mathematics and Optimization doi: 10.1007/BF01448394 – ident: 10.1016/j.nahs.2010.09.002_br000135 doi: 10.1109/CDC.2010.5718054 – volume: 99 start-page: 85 year: 2004 ident: 10.1016/j.nahs.2010.09.002_br000150 article-title: Error estimation and adaptive discretization for the discrete stochastic Hamilton–Jacobi–Bellman equation publication-title: Numerische Mathematik doi: 10.1007/s00211-004-0555-4 – volume: 15 start-page: 1 year: 1987 ident: 10.1016/j.nahs.2010.09.002_br000125 article-title: A numerical approach to the infinite horizon problem of deterministic control theory publication-title: Applied Mathematics and Optimization doi: 10.1007/BF01442644 – volume: 44 start-page: 1259 year: 2005 ident: 10.1016/j.nahs.2010.09.002_br000035 article-title: Hybrid control systems and viscosity solutions publication-title: SIAM Journal on Control and Optimization doi: 10.1137/040618072 – ident: 10.1016/j.nahs.2010.09.002_br000015 doi: 10.1109/CDC.1999.832814 – ident: 10.1016/j.nahs.2010.09.002_br000110 doi: 10.3182/20090916-3-ES-3003.00055 – volume: 41 start-page: 11 year: 2005 ident: 10.1016/j.nahs.2010.09.002_br000085 article-title: Optimal control of switching systems publication-title: Automatica – volume: 75 start-page: 319 year: 1997 ident: 10.1016/j.nahs.2010.09.002_br000090 article-title: An adaptive grid scheme for the discrete Hamilton–Jacobi–Bellman equation publication-title: Numerische Mathematik doi: 10.1007/s002110050241 – ident: 10.1016/j.nahs.2010.09.002_br000055 – ident: 10.1016/j.nahs.2010.09.002_br000020 doi: 10.1109/CDC.1999.831404 – ident: 10.1016/j.nahs.2010.09.002_br000080 doi: 10.1109/CDC.2004.1430241 – ident: 10.1016/j.nahs.2010.09.002_br000140 – ident: 10.1016/j.nahs.2010.09.002_br000075 doi: 10.3182/20090916-3-ES-3003.00053 – year: 1992 ident: 10.1016/j.nahs.2010.09.002_br000145 – year: 1992 ident: 10.1016/j.nahs.2010.09.002_br000100 – ident: 10.1016/j.nahs.2010.09.002_br000060 doi: 10.1109/CDC.1995.478514 – volume: 54 start-page: 1440 year: 2009 ident: 10.1016/j.nahs.2010.09.002_br000025_2 article-title: On the hybrid optimal control problem: theory and algorithms publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2009.2015528 – volume: 153 start-page: 567 year: 2006 ident: 10.1016/j.nahs.2010.09.002_br000045 article-title: Relaxed dynamic programming in switching systems publication-title: IEE Proceedings — Control Theory & Applications doi: 10.1049/ip-cta:20050094 – volume: 29 start-page: 28 year: 2009 ident: 10.1016/j.nahs.2010.09.002_br000010 article-title: Hybrid dynamical systems publication-title: IEEE Control Systems Magazine doi: 10.1109/MCS.2008.931718 – start-page: 123 year: 2006 ident: 10.1016/j.nahs.2010.09.002_br000070 article-title: Optimality zone algorithms for hybrid systems: efficient algorithms for optimal location and control computation – ident: 10.1016/j.nahs.2010.09.002_br000050 doi: 10.1016/S1474-6670(17)36459-5 |
| SSID | ssj0059284 |
| Score | 1.9880644 |
| Snippet | This contribution extends a numerical method for solving optimal control problems by dynamic programming to a class of hybrid dynamic systems with autonomous... |
| SourceID | proquest crossref elsevier |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 254 |
| SubjectTerms | Approximation Discretization Dynamic programming Dynamical systems Dynamics Errors Hybrid systems Mathematical analysis Mathematical models Nonlinear dynamics Numerical analysis Optimal control Value function |
| Title | A numerical method for hybrid optimal control based on dynamic programming |
| URI | https://dx.doi.org/10.1016/j.nahs.2010.09.002 https://www.proquest.com/docview/875091037 |
| Volume | 5 |
| WOSCitedRecordID | wos000302581600012&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 issn: 1751-570X databaseCode: AIEXJ dateStart: 20070301 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0059284 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LaxsxEBZt0kN7CH3SpA906M1ssKXVSjqakpCG1i0kLb6JlSWlCY4csnZI_n1Gj10vKQ1toZfFrL2S0XyamZU-fYPQByc1d7XRBbehhJkbiUJoqYvScMhutazKeG7tx2c-mYjpVH7L5VKbWE6Aey-ur-XFfzU13ANjh6Ozf2HurlG4AZ_B6HAFs8P1jww_HvhV2oaZ5_rQkUr48yaczRoswEWcR02QRFEPUcyEHQOTStO3hK3zNqTlxHWSJDXqQLlMMia7g4PUZNMTPY-ceX9ykoAQi4mf1t1XRxDfmpZQ9nVeu_6aQ1hEZf01h-4wzJp5FHwnZ6OC8eG071xZD0Ok7yiTdHSOuSRV6vnFnaeVhbNdX0dp9UDDC_KiZB28OkrhUeg-9B43LCpBH6JNwpkET7c5_rQ3PWzjM5Mk1qHu_m4-SpVYf3d7-l26cidwx2zk-Cnayq8ReJzM_ww9sP45evKl0-BtXqDDMe6AgBMQMAABJyDgDAScgYAjEPDC4wwE3APCS_R9f-_440GRK2cUM0rJsgA37QyjljBDqWDOaS0c01zDBLRlJUpquIZJoxmpdEXrYWmdFZCL1hJS8tLSV2jDL7x9jfCwcvDKSY1gxJS8dtpVkjESZZkqIfQ2GrUDpGZZVj5UN5mrlj94psKgqjCoaigVDOo2GnTPXCRRlXt_zdpxVzktTOmeApjc-xxujaTAZ4aNsNrbxapRIqXJlO_8Y9Nv0OP1tHiLNpaXK_sOPZpdLU-by_cZcLfVW5Sz |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+numerical+method+for+hybrid+optimal+control+based+on+dynamic+programming&rft.jtitle=Nonlinear+analysis.+Hybrid+systems&rft.au=Rungger%2C+Matthias&rft.au=Stursberg%2C+Olaf&rft.date=2011-05-01&rft.pub=Elsevier+Ltd&rft.issn=1751-570X&rft.volume=5&rft.issue=2&rft.spage=254&rft.epage=274&rft_id=info:doi/10.1016%2Fj.nahs.2010.09.002&rft.externalDocID=S1751570X10000683 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1751-570X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1751-570X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1751-570X&client=summon |