A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems

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.

KEYWORDS:

• Singular optimal control problem
• feedback rule
• Legendre–Gauss–Radau pseudospectral method
• mixed-binary non-linear programming

Acknowledgments

The authors are very grateful to three anonymous referees for carefully reading this paper and for their comments and suggestions which have improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.