Synthesizing Control Laws from Data using Sum-of-Squares Optimization

TL;DR

This paper introduces a data-driven method combining Koopman operator theory, CLFs, and SOS optimization to synthesize polynomial controllers directly from data, demonstrated on an inverted pendulum.

Contribution

It presents a novel approach that bypasses system identification by directly using data to synthesize controllers via SOS optimization and Koopman theory.

Findings

Successfully stabilized an inverted pendulum using the proposed method.

Demonstrated the effectiveness of data-driven SOS-based control synthesis.

Provided a flexible framework applicable to various control problems.

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.