Inverse Optimal Feedback and Gain Margins for Unicycle Stabilization

Fuente: arXiv
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Main Authors: Kim, Kwang Hak, Todorovski, Velimir, Krstić, Miroslav
Format: Preprint
Published: 2025
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_version_ 1866916979106906112
author Kim, Kwang Hak
Todorovski, Velimir
Krstić, Miroslav
author_facet Kim, Kwang Hak
Todorovski, Velimir
Krstić, Miroslav
contents The recent development of globally strict control Lyapunov functions (CLFs) for the challenging unicycle parking problem provides a foundation for pursuing optimality. We address this in the inverse optimal framework, thereby avoiding the need to solve the Hamilton$\unicode{x2013}$Jacobi$\unicode{x2013}$Bellman (HJB) equations, and establish a general result that is optimal with respect to a meaningful cost. We present several design examples that impose varying levels of penalty on the control effort, including arbitrarily bounded control. Furthermore, we show that the inverse optimal controller possesses an infinite gain margin thanks to the system being driftless, and leveraging this property, we extend the design to an adaptive controller that handles model uncertainty. Finally, we compare the performance of the non-adaptive inverse optimal controller with its adaptive counterpart.
format Preprint
id arxiv_https___arxiv_org_abs_2509_25563
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Inverse Optimal Feedback and Gain Margins for Unicycle Stabilization
Kim, Kwang Hak
Todorovski, Velimir
Krstić, Miroslav
Optimization and Control
Systems and Control
The recent development of globally strict control Lyapunov functions (CLFs) for the challenging unicycle parking problem provides a foundation for pursuing optimality. We address this in the inverse optimal framework, thereby avoiding the need to solve the Hamilton$\unicode{x2013}$Jacobi$\unicode{x2013}$Bellman (HJB) equations, and establish a general result that is optimal with respect to a meaningful cost. We present several design examples that impose varying levels of penalty on the control effort, including arbitrarily bounded control. Furthermore, we show that the inverse optimal controller possesses an infinite gain margin thanks to the system being driftless, and leveraging this property, we extend the design to an adaptive controller that handles model uncertainty. Finally, we compare the performance of the non-adaptive inverse optimal controller with its adaptive counterpart.
title Inverse Optimal Feedback and Gain Margins for Unicycle Stabilization
topic Optimization and Control
Systems and Control
url https://arxiv.org/abs/2509.25563