The paper formulates and analyzes the linear exponential quadratic Gaussian (LEQG) covariance steering problem in continuous time over a finite horizon. It shows that the optimal controller, still a linear state feedback, cannot be expressed in closed form but is parameterized by a symmetric matrix solving an algebraic equation that captures the risk‑sensitivity parameter. The authors demonstrate that this controller generalizes the risk‑neutral case and prove existence‑uniqueness of solutions near the known risk‑neutral solution for matched noise and input channels, illustrated with a numerical example.
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