Admissibility-Preserving Control for Multi-Input Systems with Joint Capacity Constraints
Abstract
This paper addresses the control of multi-input strict-feedback nonlinear systems subject to a joint capacity constraint, in which the admissible input set is a coupled subset of the individual actuator limits. Unlike existing constraint-handling methods that enforce actuator bounds channel by channel and may unnecessarily suppress admissible control directions, we develop an Anisotropic Joint-Admissibility-Preserving Input Realization (AJ-APIR) framework that explicitly exploits the geometry of the joint constraint. The proposed realization constructs a state-dependent gain matrix whose spectral decomposition separates the commanded input into normal and tangential directions relative to the constraint boundary. The normal component is attenuated as the boundary is approached, while the tangential component is preserved, which allows the admissible control effort to be redistributed without loss of tracking authority. Integrated with a backstepping controller, the AJ-APIR framework guarantees forward invariance of the joint admissible set for all time. We establish exponential convergence of the tracking error to zero together with uniform boundedness of all closed-loop signals, and characterize the resulting command-demand behavior under the joint constraint. Simulation results for a representative second-order, two-input nonlinear system subject to a power-budget constraint demonstrate the efficacy of the proposed method to enforce the joint input constraint.
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BibTeX
@misc{kumar2026admissibilitypreserving,
title = {{Admissibility-Preserving Control for Multi-Input Systems with Joint Capacity Constraints}},
author = {Saurabh Kumar and Lohitvel Gopikannan and Shashi Ranjan Kumar and Abhinav Sinha},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00533},
eprint = {2610.00533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00533},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Admissibility-Preserving Control for Multi-Input Systems with Joint Capacity Constraints
AU - Saurabh Kumar
AU - Lohitvel Gopikannan
AU - Shashi Ranjan Kumar
AU - Abhinav Sinha
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00533
UR - https://arxiv.org/abs/2610.00533
AB - This paper addresses the control of multi-input strict-feedback nonlinear systems subject to a joint capacity constraint, in which the admissible input set is a coupled subset of the individual actuator limits. Unlike existing constraint-handling methods that enforce actuator bounds channel by channel and may unnecessarily suppress admissible control directions, we develop an Anisotropic Joint-Admissibility-Preserving Input Realization (AJ-APIR) framework that explicitly exploits the geometry of the joint constraint. The proposed realization constructs a state-dependent gain matrix whose spectral decomposition separates the commanded input into normal and tangential directions relative to the constraint boundary. The normal component is attenuated as the boundary is approached, while the tangential component is preserved, which allows the admissible control effort to be redistributed without loss of tracking authority. Integrated with a backstepping controller, the AJ-APIR framework guarantees forward invariance of the joint admissible set for all time. We establish exponential convergence of the tracking error to zero together with uniform boundedness of all closed-loop signals, and characterize the resulting command-demand behavior under the joint constraint. Simulation results for a representative second-order, two-input nonlinear system subject to a power-budget constraint demonstrate the efficacy of the proposed method to enforce the joint input constraint.
ER -