Linear Exponential Quadratic Gaussian Covariance Steering

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.

Optimization and Control (math.OC); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Systems and Control (eess.SY); Machine Learning (stat.ML)

arXiv:2609.12463 [math.OC]

(or arXiv:2609.12463v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2609.12463 arXiv-issued DOI via DataCite (pending registration)