Natural Gradient Descent for Control

Ramin Esmzad; Farnaz Adib Yaghmaie; Hamidreza Modares

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arXiv · 2503.06070

Natural Gradient Descent for Control

Ramin Esmzad·Farnaz Adib Yaghmaie·Hamidreza Modares

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Abstract

This paper bridges optimization and control, and presents a novel closed-loop control framework based on natural gradient descent, offering a trajectory-oriented alternative to traditional cost-function tuning. By leveraging the Fisher Information Matrix, we formulate a preconditioned gradient descent update that explicitly shapes system trajectories. We show that, in sharp contrast to traditional controllers, our approach provides flexibility to shape the system's low-level behavior. To this end, the proposed method parameterizes closed-loop dynamics in terms of stationary covariance and an unknown cost function, providing a geometric interpretation of control adjustments. We establish theoretical stability conditions. The simulation results on a rotary inverted pendulum benchmark highlight the advantages of natural gradient descent in trajectory shaping.

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BibTeX RIS

Ramin Esmzad, Farnaz Adib Yaghmaie, Hamidreza Modares. 2025-03-08. Natural Gradient Descent for Control. https://arxiv.org/abs/2503.06070

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