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

Amin Jajarmi, Hamidreza Ramezanpour, Mohammad Dehghan Nayyeri, Ali Vahidian Kamyad
2011 Intelligent Control and Automation  
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,
more » ... of Radon measures, the problem is changed to a measure-theoretical 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.
doi:10.4236/ica.2011.22017 fatcat:aifiww5xtfhcvp4cxrrdjhaqdi