A dynamic programming approach to solving constrained linear-quadratic optimal control problems
Abstract
The solution of a constrained linear-quadratic regulator problem is determined by the set of its optimal active sets. We propose an algorithm that constructs this set of active sets for a desired horizon N from that for horizon N-1. While it is not obvious how to extend the optimal feedback law itself for horizon N-1 to horizon N, a simple relation between the optimal active sets for two successive horizon lengths exists. Specifically, every optimal active set for horizon N is a superset of an optimal active set for horizon N-1 if the constraints are ordered stage by stage. The stagewise treatment results in a favorable computational effort. In addition, it is easy to detect the solution of the current horizon is equal to the infinite-horizon solution, if such a finite horizon exists, with the proposed algorithm.
Cite
@article{arxiv.1910.11231,
title = {A dynamic programming approach to solving constrained linear-quadratic optimal control problems},
author = {Ruth Mitze and Martin Mönnigmann},
journal= {arXiv preprint arXiv:1910.11231},
year = {2020}
}