Admissibility-Preserving Constraint Lifting for Conditional Deadbeat Control of Discrete-Time Nonlinear Systems
Abstract
This paper presents a constraint-enforcing control framework for a class of discrete-time strict- feedback nonlinear systems. The objective is to guarantee closed-loop stability while ensuring forward invariance of a prescribed safe set defined by state constraints. The pro- posed approach transforms the constrained control problem into an equivalent unconstrained one through smooth constraint-lifting mappings constructed using strictly increasing sigmoid functions. Controller synthesis is then performed in the lifted coordinates, enabling recursive backstepping design while preserving the admissibility of the constrained states. Conditions on the controller gains are derived to guarantee both asymptotic stability of the closed-loop system and forward invariance of the admissible domain of the lifting functions. The analysis also establishes a conditional deadbeat property for the second backstepping step once the system trajectory enters a region in which the lifting-domain admissibility conditions are satisfied. Numerical simulations of a constrained Roup oscillator demonstrate the effectiveness of the proposed method in enforcing state constraints while tracking a reference command.
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BibTeX
@misc{delgado2026admissibilitypreserving,
title = {{Admissibility-Preserving Constraint Lifting for Conditional Deadbeat Control of Discrete-Time Nonlinear Systems}},
author = {Jhon Manuel Portella Delgado and Ankit Goel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16109},
eprint = {2610.16109},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16109},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Admissibility-Preserving Constraint Lifting for Conditional Deadbeat Control of Discrete-Time Nonlinear Systems
AU - Jhon Manuel Portella Delgado
AU - Ankit Goel
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16109
UR - https://arxiv.org/abs/2610.16109
AB - This paper presents a constraint-enforcing control framework for a class of discrete-time strict- feedback nonlinear systems. The objective is to guarantee closed-loop stability while ensuring forward invariance of a prescribed safe set defined by state constraints. The pro- posed approach transforms the constrained control problem into an equivalent unconstrained one through smooth constraint-lifting mappings constructed using strictly increasing sigmoid functions. Controller synthesis is then performed in the lifted coordinates, enabling recursive backstepping design while preserving the admissibility of the constrained states. Conditions on the controller gains are derived to guarantee both asymptotic stability of the closed-loop system and forward invariance of the admissible domain of the lifting functions. The analysis also establishes a conditional deadbeat property for the second backstepping step once the system trajectory enters a region in which the lifting-domain admissibility conditions are satisfied. Numerical simulations of a constrained Roup oscillator demonstrate the effectiveness of the proposed method in enforcing state constraints while tracking a reference command.
ER -