A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems
This paper presents a new approach for the efficient solution of singular optimal control problems (SOCPs). A novel feature of the proposed method is that it does not require a priori knowledge of the structure of solution. At first, the SOCP is converted into a binary optimal control problem. Then,...
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| Vydané v: | International journal of control Ročník 92; číslo 7; s. 1551 - 1566 |
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| Jazyk: | English |
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Taylor & Francis
03.07.2019
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| Abstract | This paper presents a new approach for the efficient solution of singular optimal control problems (SOCPs). A novel feature of the proposed method is that it does not require a priori knowledge of the structure of solution. At first, the SOCP is converted into a binary optimal control problem. Then, by utilising the pseudospectral method, the resulting problem is transcribed to a mixed-binary non-linear programming problem. This mixed-binary non-linear programming problem, which can be solved by well-known solvers, allows us to detect the structure of the optimal control and to compute the approximating solution. The main advantages of the present method are that: (1) without a priori information, the structure of optimal control is detected; (2) it produces good results even using a small number of collocation points; (3) the switching times can be captured accurately. These advantages are illustrated through a numerical implementation of the method on four examples. |
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| AbstractList | This paper presents a new approach for the efficient solution of singular optimal control problems (SOCPs). A novel feature of the proposed method is that it does not require a priori knowledge of the structure of solution. At first, the SOCP is converted into a binary optimal control problem. Then, by utilising the pseudospectral method, the resulting problem is transcribed to a mixed-binary non-linear programming problem. This mixed-binary non-linear programming problem, which can be solved by well-known solvers, allows us to detect the structure of the optimal control and to compute the approximating solution. The main advantages of the present method are that: (1) without a priori information, the structure of optimal control is detected; (2) it produces good results even using a small number of collocation points; (3) the switching times can be captured accurately. These advantages are illustrated through a numerical implementation of the method on four examples. |
| Author | Foroozandeh, Z. Shamsi, M. de Pinho, M. d. R. |
| Author_xml | – sequence: 1 givenname: Z. surname: Foroozandeh fullname: Foroozandeh, Z. organization: Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology – sequence: 2 givenname: M. surname: Shamsi fullname: Shamsi, M. email: m_shamsi@aut.ac.ir organization: Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology – sequence: 3 givenname: M. d. R. surname: de Pinho fullname: de Pinho, M. d. R. organization: Department of Electrical and Computer Engineering, SYSTEC, Faculdade de Engenharia, Universidade do Porto |
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| Cites_doi | 10.23919/ECC.2003.7084970 10.1007/0-387-30065-1_4 10.1137/1.9781611972368 10.1002/mma.4097 10.1109/CDC.2009.5400735 10.1145/365723.365727 10.1007/s10957-008-9387-1 10.1080/10556780310001656637 10.1016/0005-1098(68)90006-X 10.1093/oso/9780198506720.001.0001 10.1007/s40995–017–0176–2 10.1016/j.arcontrol.2012.09.002 10.1137/0328047 10.1137/S0036142993295545 10.1007/s10957-012-0254-8 10.1017/CBO9780511626357 10.1137/S1064827501388182 10.1002/oca.814 10.1007/BF00935706 10.1137/0315019 10.1109/CDC.2013.6759933 10.2514/1.20478 10.1007/978-3-540-46783-0 10.1023/A:1021708729556 10.2514/3.59765 10.1109/9.467672 10.1016/0167-6911(87)90024-7 10.1080/00207179.2015.1088173 10.1007/BF00940625 10.1137/110822177 10.1016/j.automatica.2015.11.035 10.1007/BF02359231 10.1109/CDC.2016.7798271 10.1109/TAC.2006.878570 10.1080/00207179308934376 10.1007/BF00941825 10.1109/9.173155 10.2514/1.37387 10.1007/978-1-4757-2135-5_22 10.1016/j.isatra.2009.10.002 10.1007/s10957-016-0909-y 10.1080/00207179.2015.1126356 10.1007/s10957-009-9594-4 10.1038/105809a0 10.1137/1.9780898718577 10.1002/oca.967 10.1137/0318002 10.1016/S1385-8947(99)00019-4 10.1007/978-3-662-04331-8_2 10.1007/BF00933131 10.1080/00207177208932258 10.1080/00207177308932423 10.2514/2.4709 10.3934/mbe.2011.8.307 10.1016/j.jfranklin.2014.07.005 10.1016/j.automatica.2010.06.048 |
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| SubjectTerms | Economic models feedback rule Legendre-Gauss-Radau pseudospectral method Linear programming Mathematical programming mixed-binary non-linear programming Nonlinear programming Optimal control Singular optimal control problem Solvers Spectral methods |
| Title | A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems |
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