Iterative Learning Control of Fast, Nonlinear, Oscillatory Dynamics (Preprint)

TL;DR

This paper introduces a novel iterative control method combining trajectory optimization, phase portraits, and Gaussian processes to stabilize fast, nonlinear, oscillatory systems despite slow controllers, demonstrated on the Lorenz system.

Contribution

It develops a new control framework that enables low-speed controllers to manage fast, nonlinear oscillatory dynamics using iterative learning and parameter tuning.

Findings

Successfully controls Lorenz system to reproduce desired oscillations

Demonstrates robustness to missing information and uncontrollable parameters

Identifies stable regions of control parameters for system stability

Abstract

The sudden onset of deleterious and oscillatory dynamics (often called instabilities) is a known challenge in many fluid, plasma, and aerospace systems. These dynamics are difficult to address because they are nonlinear, chaotic, and are often too fast for active control schemes. In this work, we develop an alternative active controls system using an iterative, trajectory-optimization and parameter-tuning approach based on Iterative Learning Control (ILC), Time-Lagged Phase Portraits (TLPP) and Gaussian Process Regression (GPR). The novelty of this approach is that it can control a system's dynamics despite the controller being much slower than the dynamics. We demonstrate this controller on the Lorenz system of equations where it iteratively adjusts (tunes) the system's input parameters to successfully reproduce a desired oscillatory trajectory or state. Additionally, we investigate the system's dynamical sensitivity to its control parameters, identify continuous and bounded regions of desired dynamical trajectories, and demonstrate that the controller is robust to missing information and uncontrollable parameters as long as certain requirements are met. The controller presented in this work provides a framework for low-speed control for a variety of fast, nonlinear systems that may aid in instability suppression and mitigation.