Trajectory-Oriented Control Using Gradient Descent: An Unconventional Approach
Abstract
In this work, we introduce a novel gradient descent-based approach for optimizing control systems, leveraging a new representation of stable closed-loop dynamics as a function of two matrices i.e. the step size or direction matrix and value matrix of the Lyapunov cost function. This formulation provides a new framework for analyzing and designing feedback control laws. We show that any stable closed-loop system can be expressed in this form with appropriate values for the step size and value matrices. Furthermore, we show that this parameterization of the closed-loop system is equivalent to a linear quadratic regulator for appropriately chosen weighting matrices. We also show that trajectories can be shaped using this approach to achieve a desired closed-loop behavior.
Cite
@article{arxiv.2409.10662,
title = {Trajectory-Oriented Control Using Gradient Descent: An Unconventional Approach},
author = {Ramin Esmzad and Hamidreza Modares},
journal= {arXiv preprint arXiv:2409.10662},
year = {2024}
}