A Behavioral approach to Constrained Linear Quadratic Control: Feasibility and Optimality
Abstract
This paper develops a constrained linear-quadratic (LQ) optimal control framework within the behavioral approach. Unlike classical formulations that rely on state-input representations, our method treats both the system dynamics and the constraints as trajectory-level objects. The system is modeled through a kernel representation, while inequality constraints are captured using behavioral inequalities defined over infinite-dimensional convex cones. Using quadratic differential forms (QDFs) to encode performance indices, we formulate the constrained LQ problem as a convex variational optimization over trajectories. By employing Gateaux differentials, we derive the stationarity and complementarity conditions and show that they admit a representation as an augmented behavioral system whose unique decomposition into autonomous and controllable sub-behaviors yields a complete parameterization of all optimal constrained trajectories. The resulting conditions constitute a behavioral analogue of the Karush-Kuhn-Tucker (KKT) framework. A numerical example illustrates the effect of inequality constraints on the optimal behavior. The framework provides a general, trajectory-level representation for constrained optimal control and opens avenues for closed-loop and data-driven extensions.
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BibTeX
@misc{bandyopadhyay2026behavioral,
title = {{A Behavioral approach to Constrained Linear Quadratic Control: Feasibility and Optimality}},
author = {Soutrik Bandyopadhyay and Debasattam Pal and Shubhendu Bhasin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40542},
eprint = {2610.40542},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40542},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A Behavioral approach to Constrained Linear Quadratic Control: Feasibility and Optimality
AU - Soutrik Bandyopadhyay
AU - Debasattam Pal
AU - Shubhendu Bhasin
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40542
UR - https://arxiv.org/abs/2610.40542
AB - This paper develops a constrained linear-quadratic (LQ) optimal control framework within the behavioral approach. Unlike classical formulations that rely on state-input representations, our method treats both the system dynamics and the constraints as trajectory-level objects. The system is modeled through a kernel representation, while inequality constraints are captured using behavioral inequalities defined over infinite-dimensional convex cones. Using quadratic differential forms (QDFs) to encode performance indices, we formulate the constrained LQ problem as a convex variational optimization over trajectories. By employing Gateaux differentials, we derive the stationarity and complementarity conditions and show that they admit a representation as an augmented behavioral system whose unique decomposition into autonomous and controllable sub-behaviors yields a complete parameterization of all optimal constrained trajectories. The resulting conditions constitute a behavioral analogue of the Karush-Kuhn-Tucker (KKT) framework. A numerical example illustrates the effect of inequality constraints on the optimal behavior. The framework provides a general, trajectory-level representation for constrained optimal control and opens avenues for closed-loop and data-driven extensions.
ER -