Trajectory-Oriented Control Using Gradient Descent: An Unconventional Approach
<|reference_start|>Trajectory-Oriented Control Using Gradient Descent: An Unconventional Approach: 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.<|reference_end|>
@article{esmzad2024trajectory-oriented,
    title={Trajectory-Oriented Control Using Gradient Descent: An Unconventional
  Approach},
    author={Ramin Esmzad, Hamidreza Modares},
    journal={arXiv preprint arXiv:2409.10662},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.10662},
    primaryClass={math.OC cs.SY eess.SY}
}