Skip to content
DraconiticResearch
Search Sources API
186,125 studies31 sourcesUpdated 28 min ago
PreprintCC BY 4.0arXiv

Linear Exponential Quadratic Gaussian Covariance Steering

  • Chiran B. Cherian
  • Yasemin Isik
  • Abhishek Halder
Open at sourcePDFDOICite

Abstract

We formulate and analyze the linear exponential quadratic Gaussian (LEQG) covariance steering problem in continuous time over a given deadline (finite time horizon). The solution for this problem can be seen as a risk-sensitive Schrödinger bridge between Gaussian endpoints in the linear quadratic setting. Unlike the risk-neutral case, the LEQG covariance steering controller--still a linear state feedback--can no longer be written in closed form. We show that the optimal controller is parameterized by a symmetric matrix solving an algebraic equation that encodes the implicit dependence on the risk-sensitivity parameter. We explain how the structure of this optimal controller significantly generalizes the existing results for the risk-neutral case. Building on these results, for the matched noise and input channel case, we prove the existence-uniqueness of solution for the LEQG covariance steering problem in the neighborhood of the known risk-neutral optimal solution. We give an illustrative numerical example.

Related

  1. No Spurious Local Minima in Full-Order Linear Quadratic Gaussian Control
    Yang Zheng, Yujie Tang
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  2. Distributionally Robust Adaptive Iterative Covariance Steering for Small-Body Proximity Operations
    Vivek Khatana, Aditya Gahlawat, Naira Hovakimyan +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv
  3. Cubature-Based Statistical Moment Steering for Nonlinear, Non-Gaussian Trajectory Optimization
    Daniel C. Qi, Kenshiro Oguri
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  4. Tracy Widom law for sample covariance matrices under quadratic form concentration
    Guangchen Chen, Xing Lyu
    arXivPreprintCC0Full textMathematical physicsProbabilityarXiv
  5. Addendum to "Optimal Steering of a Linear Stochastic System to a Final Probability Distribution, Part II"
    Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{cherian2026linear,
  title = {{Linear Exponential Quadratic Gaussian Covariance Steering}},
  author = {Chiran B. Cherian and Yasemin Isik and Abhishek Halder},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12463},
  eprint = {2609.12463},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12463},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Linear Exponential Quadratic Gaussian Covariance Steering
AU  - Chiran B. Cherian
AU  - Yasemin Isik
AU  - Abhishek Halder
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12463
UR  - https://arxiv.org/abs/2609.12463
AB  - We formulate and analyze the linear exponential quadratic Gaussian (LEQG) covariance steering problem in continuous time over a given deadline (finite time horizon). The solution for this problem can be seen as a risk-sensitive Schrödinger bridge between Gaussian endpoints in the linear quadratic setting. Unlike the risk-neutral case, the LEQG covariance steering controller--still a linear state feedback--can no longer be written in closed form. We show that the optimal controller is parameterized by a symmetric matrix solving an algebraic equation that encodes the implicit dependence on the risk-sensitivity parameter. We explain how the structure of this optimal controller significantly generalizes the existing results for the risk-neutral case. Building on these results, for the matched noise and input channel case, we prove the existence-uniqueness of solution for the LEQG covariance steering problem in the neighborhood of the known risk-neutral optimal solution. We give an illustrative numerical example.
ER  -