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.

翻译：有害振荡动力学（常称为不稳定性）的突然出现是许多流体、等离子体和航空航天系统中已知的挑战。这些动力学难以处理，因为它们是非线性、混沌的，并且通常过于快速而难以实施主动控制方案。在本工作中，我们基于迭代学习控制（ILC）、时滞相图（TLPP）和高斯过程回归（GPR），采用一种迭代的轨迹优化与参数整定方法，开发了一种替代性的主动控制系统。该方法的新颖之处在于，即使控制器的速度远慢于被控动力学，它仍能实现对系统动力学的控制。我们在洛伦兹方程系统上验证了该控制器，它通过迭代调整（整定）系统的输入参数，成功复现了期望的振荡轨迹或状态。此外，我们研究了系统动力学对其控制参数的敏感性，识别了期望动力学轨迹的连续有界区域，并证明了只要满足特定条件，该控制器对信息缺失和不可控参数具有鲁棒性。本工作提出的控制器为各类快速非线性系统提供了一种低速控制框架，可能有助于不稳定性的抑制与缓解。