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On representation formulas for optimal control: A Lagrangian perspective
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- Authors
- Issue Date
- 2022-11
- Citation
- IET Control Theory and Applications, Vol.16 No.16, pp.1633-1644
- 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.
- ISSN
- 1751-8644
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