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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Vydáno v:International journal of control Ročník 92; číslo 7; s. 1551 - 1566
Hlavní autoři: Foroozandeh, Z., Shamsi, M., de Pinho, M. d. R.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 03.07.2019
Taylor & Francis Ltd
Témata:
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
ISSN:0020-7179, 1366-5820
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Shrnutí: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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ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2017.1399216