aiqbench analysis
This research advances the theoretical foundations of risk-sensitive control by framing covariance steering as a Schrödinger bridge problem within linear exponential quadratic Gaussian systems. The study demonstrates that while optimal controllers remain linear state feedback, their structure becomes implicitly defined by algebraic equations dependent on risk parameters, generalizing existing risk-neutral frameworks. These findings are critical for developing robust AI agents and quantum control protocols that must operate under specific uncertainty constraints over finite time horizons.
Linear Exponential Quadratic Gaussian Covariance Steering
arXiv:2609.12463v1 Announce Type: cross 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 Schr\"{o}dinger 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.
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)
Full text under the publisher's open licence · 178 words
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