Min-max piecewise constant optimal control for multi-model linear systems
Abstract
The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set (i.e., there exist only finitely many possible models for the plant). Uncertainty is dealt with using a min-max approach (i.e., we seek the best control for the worst possible plant). The optimal control is derived using a multi-model version of Lagrange's multipliers method, which specifies the control in terms of a discrete-time Riccati equation and an optimization problem over a simplex. A numerical algorithm for computing the optimal control is proposed and tested by simulation.
Cite
@article{arxiv.1412.3861,
title = {Min-max piecewise constant optimal control for multi-model linear systems},
author = {Félix A. Miranda and Fernando Castaños and Alexander Poznyak},
journal= {arXiv preprint arXiv:1412.3861},
year = {2021}
}
Comments
20 pages, 8 figures. Submitted to IMA Journal of Mathematical Control and Applications