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PreprintarXiv licencearXiv

Open-Loop Stackelberg LQ Difference Games with Coupled-Affine Inequality Constraints: An Exact OCP--LCS/LCQP Reformulation

  • Shrestha Ghosh
  • Puduru Viswanadha Reddy
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Abstract

In this letter, we study finite-horizon linear-quadratic Stackelberg difference games with coupled-affine state-control inequality constraints. Under the stated assumptions, we show that generalized open-loop Stackelberg equilibria admit an exact reformulation as an optimal control problem subject to a discrete-time linear complementarity system. Eliminating the dynamic variables yields a large-scale linear complementarity quadratic program, together with an explicit recovery map for the follower strategy. This reformulation enables the numerical computation of these equilibria. We illustrate the proposed approach using a constrained network-flow game.

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Cite

BibTeXRIS
BibTeX
@misc{ghosh2026openloop,
  title = {{Open-Loop Stackelberg LQ Difference Games with Coupled-Affine Inequality Constraints: An Exact OCP--LCS/LCQP Reformulation}},
  author = {Shrestha Ghosh and Puduru Viswanadha Reddy},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04928},
  eprint = {2609.04928},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04928},
}
RIS
TY  - UNPB
TI  - Open-Loop Stackelberg LQ Difference Games with Coupled-Affine Inequality Constraints: An Exact OCP--LCS/LCQP Reformulation
AU  - Shrestha Ghosh
AU  - Puduru Viswanadha Reddy
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.04928
UR  - https://arxiv.org/abs/2609.04928
AB  - In this letter, we study finite-horizon linear-quadratic Stackelberg difference games with coupled-affine state-control inequality constraints. Under the stated assumptions, we show that generalized open-loop Stackelberg equilibria admit an exact reformulation as an optimal control problem subject to a discrete-time linear complementarity system. Eliminating the dynamic variables yields a large-scale linear complementarity quadratic program, together with an explicit recovery map for the follower strategy. This reformulation enables the numerical computation of these equilibria. We illustrate the proposed approach using a constrained network-flow game.
ER  -