Synthesizing Control Laws from Data using Sum-of-Squares Optimization
Abstract
The control Lyapunov function (CLF) approach to nonlinear control design is well established. Moreover, when the plant is control affine and polynomial, sum-of-squares (SOS) optimization can be used to find a polynomial controller as a solution to a semidefinite program. This letter considers the use of data-driven methods to design a polynomial controller by leveraging Koopman operator theory, CLFs, and SOS optimization. First, Extended Dynamic Mode Decomposition (EDMD) is used to approximate the Lie derivative of a given CLF candidate with polynomial lifting functions. Then, the polynomial Koopman model of the Lie derivative is used to synthesize a polynomial controller via SOS optimization. The result is a flexible data-driven method that skips the intermediary process of system identification and can be applied widely to control problems. The proposed approach is used to successfully synthesize a controller to stabilize an inverted pendulum on a cart.
Keywords
Cite
@article{arxiv.2307.01089,
title = {Synthesizing Control Laws from Data using Sum-of-Squares Optimization},
author = {Jason J. Bramburger and Steven Dahdah and James Richard Forbes},
journal= {arXiv preprint arXiv:2307.01089},
year = {2024}
}