Linear covariance control improves risk-sensitive system steering
Linear Exponential Quadratic Gaussian Covariance Steering
Artificial IntelligenceMachine Learning
Summary
Controlling a system's uncertain behavior over time is important in many applications. This paper looks at steering the system so that its randomness matches desired end conditions while accounting for risk sensitivity, meaning the controller is cautious about uncertainties. The authors provide a new mathematical way to find the best controller that adapts to risk concerns, extending previous simpler cases that ignored risk. They prove the solution exists near known risk-neutral solutions and show an example of how it works.
What this means in practice
- •For autonomous vehicle engineers: Design controllers that cautiously steer vehicle states while managing uncertainty and safety limits during operation deadlines.
- •For robotics control teams: Implement feedback controllers that shape robot behavior to meet precise state targets while being sensitive to sensing and actuation risk.
Authors
Chiran B. Cherian, Yasemin Isik, Abhishek Halder
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.