# Linear genetic programming control for strongly nonlinear dynamics with frequency crosstalk

## TL;DR

This paper introduces Linear Genetic Programming Control (LGPC), a model-free method that effectively exploits frequency crosstalk in nonlinear dynamics for control tasks, demonstrated on oscillator stabilization and turbulence drag reduction.

## Contribution

The paper presents LGPC, a novel linear genetic programming approach for control of strongly nonlinear systems with multiple actuators and sensors, generalizing previous machine learning control methods.

## Key findings

- LGPC successfully stabilizes a nonlinear oscillator model.
- LGPC achieves 22% drag reduction in turbulence control.
- LGPC exploits frequency crosstalk for optimal control.

## Abstract

We advance Machine Learning Control (MLC), a recently proposed model-free control framework which explores and exploits strongly nonlinear dynamics in an unsupervised manner. The assumed plant has multiple actuators and sensors and its performance is measured by a cost functional. The control problem is to find a control logic which optimizes the given cost function. The corresponding regression problem for the control law is solved by employing linear genetic programming as an easy and simple regression solver in a high-dimensional control search space. This search space comprises open-loop actuation, sensor-based feedback and combinations thereof, thus generalizing former MLC studies. This methodology is denoted as linear genetic programming control (LGPC). Focus of this study is the frequency crosstalk between unforced unstable oscillation and the actuation at different frequencies. LGPC is first applied to the stabilization of a forced nonlinearly coupled three-oscillator model comprising open- and closed-loop frequency crosstalk mechanisms. LGPC performance is then demonstrated in a turbulence control experiment, achieving 22% drag reduction for a simplified car model. For both cases, LGPC identifies the best nonlinear control achieving the optimal performance by exploiting frequency crosstalk. Our control strategy is suited to complex control problems with multiple actuators and sensors featuring nonlinear actuation dynamics.