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arXiv · 2204.02050

On representation formulas for optimal control: A Lagrangian perspective

Yeoneung Kim·Insoon Yang
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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 $\delta$-net, as well as a numerical scheme for controller synthesis via convex optimization.

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Yeoneung Kim, Insoon Yang. 2022-04-05. On representation formulas for optimal control: A Lagrangian perspective. https://doi.org/10.1049/cth2.12329

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