On representation formulas for optimal control: A Lagrangian perspective
- Authors
- Kim, Yeoneung; Yang, Insoon
- Issue Date
- Nov-2022
- Publisher
- WILEY
- Citation
- IET CONTROL THEORY AND APPLICATIONS, v.16, no.16, pp 1633 - 1644
- Pages
- 12
- Journal Title
- IET CONTROL THEORY AND APPLICATIONS
- Volume
- 16
- Number
- 16
- Start Page
- 1633
- End Page
- 1644
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/85612
- DOI
- 10.1049/cth2.12329
- ISSN
- 1751-8644
1751-8652
- Abstract
- This paper studies the representation formulas for finite-horizon optimal control problems with or without state constraints, unifying two different viewpoints: the Lagrangian and dynamic programming frameworks. In a recent work by Lee and Tomlin [1], the generalised Lax formula is obtained via dynamic programming for optimal control problems with state constraints and non-linear systems. We revisit the formula from the Lagrangian perspective to provide a unified framework for understanding and implementing the non-trivial representation of the value function. Our simple derivation makes direct use of the Lagrangian formula from the theory of Hamilton-Jacobi 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 optimisation.
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