An hybrid system approach to nonlinear optimal control problems
Abstract
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced by piecewise affine approximations which allow an analytical resolution. The sequence of affine models then forms a sequence of states of a hybrid automaton. Given a sequence of states, we introduce an hybrid approximation of the nonlinear controllable domain and propose a new algorithm computing a controllable, piecewise convex approximation. The same way the nonlinear optimal control problem is replaced by an hybrid piecewise affine one. Stating a hybrid maximum principle suitable to our hybrid model, we deduce the global structure of the hybrid optimal control steering the system to the target.
Cite
@article{arxiv.math/0502172,
title = {An hybrid system approach to nonlinear optimal control problems},
author = {Jean-Guillaume Luc Dumas and Aude Rondepierre},
journal= {arXiv preprint arXiv:math/0502172},
year = {2008}
}