Linear Exponential Quadratic Gaussian Covariance Steering

2026-09-11

AI Summary

研究解决了连续时间下LEQG协方差导向问题，通过求解一个与风险敏感参数相关的代数方程来获得最优控制器。

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.

Problem

• Linear Exponential Quadratic Gaussian
• Covariance Steering
• Risk-Sensitivity

Innovation

• Linear Exponential Quadratic Gaussian
• Covariance Steering
• Risk-Sensitive
• Optimal Controller
• Algebraic Equation