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S. A. Alavi, A. V. Kamyad and M. Gachpazan, “Solving of Nonlinear Ordinary Differential Equations as a Control Problem by Using Measure Theory,” Scientia Iranica, Vol. 7, No. 1, 2000, pp. 1-7.

has been cited by the following article:

• TITLE: A Measure Theoretical Approach for Path Planning Problem of Nonlinear Control Systems

  AUTHORS: Amin Jajarmi, Hamidreza Ramezanpour, Mohammad Dehghan Nayyeri, Ali Vahidian Kamyad

  KEYWORDS: Path Planning, Optimal Control, Measure Theory, Linear Programming

  JOURNAL NAME: Intelligent Control and Automation, Vol.2 No.2, June 3, 2011

  ABSTRACT: This paper presents a new approach to find an approximate solution for the nonlinear path planning problem. In this approach, first by defining a new formulation in the calculus of variations, an optimal control problem, equivalent to the original problem, is obtained. Then, a metamorphosis is performed in the space of problem by defining an injection from the set of admissible trajectory-control pairs in this space into the space of positive Radon measures. Using properties of Radon measures, the problem is changed to a measure-theo- retical optimization problem. This problem is an infinite dimensional linear programming (LP), which is approximated by a finite dimensional LP. The solution of this LP is used to construct an approximate solution for the original path planning problem. Finally, a numerical example is included to verify the effectiveness of the proposed approach.