An hybrid system approach to nonlinear optimal control problems
<|reference_start|>An hybrid system approach to nonlinear optimal control problems: 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.<|reference_end|>
@article{dumas2005an,
    title={An hybrid system approach to nonlinear optimal control problems},
    author={Jean-Guillaume Luc Dumas (LJK), Aude Rondepierre (MIP)},
    journal={arXiv preprint arXiv:math/0502172},
    year={2005},
    archivePrefix={arXiv},
    eprint={math/0502172},
    primaryClass={math.OC cs.SC}
}