Inverse Optimal Feedback Stabilization of 3D Nonholonomic Vehicles in Spherical Coordinates
Abstract
Inverse optimal control provides optimality and robustness guarantees without solving the Hamilton--Jacobi--Bellman (HJB) equation, but its application to 3D nonholonomic vehicles has been precluded by the absence of strict control Lyapunov functions (CLFs). Recently, such strict CLFs were constructed for the 3D nonholonomic vehicle in spherical coordinates, which circumvent Brockett's obstruction, on the largest possible domain. Building on this construction, this paper develops a general inverse optimal stabilizing controller for the 3D nonholonomic vehicle actuated by surge velocity, pitch rate, and yaw rate. The design is a damping LgV feedback that minimizes a meaningful cost and inherits stability margins. Its flexibility is demonstrated through two choices of penalty function: a quadratic running cost on the state, recovering a near-classical optimal control formulation, and stabilization under user-defined input constraints. Numerical simulations illustrate stabilization performance, control-effort tradeoffs, and the effect of input constraints.
Related
- Global Exponential Stabilization of a 3D Nonholonomic Vehicle in Spherical Coordinates
- Spherical harmonics, operators of multiplication by coordinates, and infinitesimal conformal transformations
- Output feedback stabilization of ODE-heat and heat-ODE cascades with in-domain pointwise coupling
- Complexity of Output Feedback Stabilization
- Feedback Stabilization for Sampled Linear Systems with Control-linear Noise
BibTeX
@misc{kim2026inverse,
title = {{Inverse Optimal Feedback Stabilization of 3D Nonholonomic Vehicles in Spherical Coordinates}},
author = {Kwang Hak Kim and Mamadou Diagne and Miroslav Krstic},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36212},
eprint = {2609.36212},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36212},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inverse Optimal Feedback Stabilization of 3D Nonholonomic Vehicles in Spherical Coordinates
AU - Kwang Hak Kim
AU - Mamadou Diagne
AU - Miroslav Krstic
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36212
UR - https://arxiv.org/abs/2609.36212
AB - Inverse optimal control provides optimality and robustness guarantees without solving the Hamilton--Jacobi--Bellman (HJB) equation, but its application to 3D nonholonomic vehicles has been precluded by the absence of strict control Lyapunov functions (CLFs). Recently, such strict CLFs were constructed for the 3D nonholonomic vehicle in spherical coordinates, which circumvent Brockett's obstruction, on the largest possible domain. Building on this construction, this paper develops a general inverse optimal stabilizing controller for the 3D nonholonomic vehicle actuated by surge velocity, pitch rate, and yaw rate. The design is a damping L_gV feedback that minimizes a meaningful cost and inherits stability margins. Its flexibility is demonstrated through two choices of penalty function: a quadratic running cost on the state, recovering a near-classical optimal control formulation, and stabilization under user-defined input constraints. Numerical simulations illustrate stabilization performance, control-effort tradeoffs, and the effect of input constraints.
ER -