A modified measure theoretical approach for solving the optimal control problems Hassan Zarei Department of Mathematics, Payame Noor University, Tehran, Iran Abstract In this paper, in order to overcome the drawbacks of the Rubio’s mea- sure theoretical approach, the last step of approximation in his approach is omitted and the optimal control problems are approximated by the nonlinear programming (NLP) problems. The usefulness of the approach is confirmed by applying it on two examples. Keywords. Measure theory, Nonlinear programming, CML model 1 Introduction The measure theoretical-based approach for approximating an optimal control problem by a linear programming (LP) one, which has been theoretically es- tablished by Rubio [4], has been applied to optimal control of the lumped and distributed parameter systems; see [5], [3] and references therein. Nevertheless, it has some drawbacks. One of them, is the use of sequential approximations on an optimal control problem which dramatically affects the precision of the method. Moreover, there are difficulties in solving the high dimensional LP problems approximating the large scale optimal control problems. The authors in [1] have used the metaheurestic algorithms to solve the NLP problem approx- imation of the classic optimal control problems obtained by the Rubio’s measure theoretical-based approach. Motivated by their work and in order to overcome the mentioned drawbacks, in the next section we briefly review the measure the- oretical approach to approximate the optimal control problems with the NLP ones and we give a system of nonlinear equations as the necessary optimality conditions which can be easily solved by using the optimization softwares such as the MATLAB optimization toolbox. The efficiency of the method is demon- strated through the two numerical experiments, in section 3. The last section is the conclusion. 1 AMO - Advanced Modeling and Optimization, Volume 20, Number 1, 2018 211 211 AMO - Advanced Modeling and Optimization. ISSN: 1841-4311 * Corresponding Author * zarei2003@gmail.com