Optimal Control for Nonlinear Hybrid Systems via Convex Relaxations
Abstract
This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of physical systems undergoing contact, the construction of a numerical method for their optimal control has proven challenging due to the combinatorial nature of the state-dependent switching and the potential discontinuities that arise during switches. This paper constructs a convex relaxation-based approach to solve this optimal control problem. Our approach begins by formulating the problem in the space of relaxed controls, which gives rise to a linear program whose solution is proven to compute the globally optimal controller. This conceptual program is solved by constructing a sequence of semidefinite programs whose solutions are proven to converge from below to the true solution of the original optimal control problem. Finally, a method to synthesize the optimal controller is developed. Using an array of examples, the performance of the proposed method is validated on problems with known solutions and also compared to a commercial solver.
Cite
@article{arxiv.1702.04310,
title = {Optimal Control for Nonlinear Hybrid Systems via Convex Relaxations},
author = {Pengcheng Zhao and Shankar Mohan and Ram Vasudevan},
journal= {arXiv preprint arXiv:1702.04310},
year = {2018}
}