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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| Veröffentlicht in: | International journal of control Jg. 92; H. 7; S. 1551 - 1566 |
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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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| 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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