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

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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.

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A. Jajarmi, H. Ramezanpour, M. Nayyeri and A. Kamyad, "A Measure Theoretical Approach for Path Planning Problem of Nonlinear Control Systems,"

*Intelligent Control and Automation*, Vol. 2 No. 2, 2011, pp. 144-151. doi: 10.4236/ica.2011.22017.

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