On representation formulas for optimal control: A Lagrangian perspective
Abstract
In this paper, we study representation formulas for finite-horizon optimal control problems with or without state constraints, unifying two different viewpoints: the Lagrangian and dynamic programming (DP) frameworks. In a recent work [1], the generalized Lax formula is obtained via DP for optimal control problems with state constraints and nonlinear systems. We revisit the formula from the Lagrangian perspective to provide a unified framework for understanding and implementing the nontrivial representation of the value function. Our simple derivation makes direct use of the Lagrangian formula from the theory of Hamilton-Jacobi (HJ) equations. We also discuss a rigorous way to construct an optimal control using a -net, as well as a numerical scheme for controller synthesis via convex optimization.
Cite
@article{arxiv.2204.02050,
title = {On representation formulas for optimal control: A Lagrangian perspective},
author = {Yeoneung Kim and Insoon Yang},
journal= {arXiv preprint arXiv:2204.02050},
year = {2022}
}