Measures and LMIs for optimal control of piecewise-affine systems
Abstract
This paper considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector field, polynomial Lagrangian and semialgebraic input and state constraints. The OCP is first relaxed as an infinite-dimensional linear program (LP) over a space of occupation measures. This LP, a particular instance of the generalized moment problem, is then approached by an asymptotically converging hierarchy of linear matrix inequality (LMI) relaxations. The relaxed dual of the original LP returns a polynomial approximation of the value function that solves the Hamilton-Jacobi-Bellman (HJB) equation of the OCP. Based on this polynomial approximation, a suboptimal policy is developed to construct a state feedback in a sample-and-hold manner. The results show that the suboptimal policy succeeds in providing a stabilizing suboptimal state feedback law that drives the system relatively close to the optimal trajectories and respects the given constraints.
Keywords
Cite
@article{arxiv.1211.3318,
title = {Measures and LMIs for optimal control of piecewise-affine systems},
author = {M. Rasheed Abdalmoaty and Didier Henrion and Luis Rodrigues},
journal= {arXiv preprint arXiv:1211.3318},
year = {2012}
}