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- Title
On representation formulas for optimal control: A Lagrangian perspective.
- Authors
Kim, Yeoneung; Yang, Insoon
- 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 δ‐net, as well as a numerical scheme for controller synthesis via convex optimisation.
- Subjects
NUMERICAL control of machine tools; DYNAMIC programming; NONLINEAR systems; HAMILTON-Jacobi equations; PETRI nets
- Publication
IET Control Theory & Applications (Wiley-Blackwell), 2022, Vol 16, Issue 16, p1633
- ISSN
1751-8644
- Publication type
Article
- DOI
10.1049/cth2.12329