Collaborative Research: Multi-Scale, Multi-Rate Spatiotemporal Optimal Control with Application to Airborne Wind Energy Systems

这项研究的目的是为操作环境随时间和可控空间位置变化的新兴系统开辟新的控制策略。这些应用包括在多变的大气条件下运行的协调无人驾驶飞行器、在多变的海洋环境中运行的可重新定位的海洋水动力能系统的概念，以及在风随时间和垂直位置变化的大气环境中运行的机载风能系统。这项研究将集中于得出与各种应用相关的一般理论，以及在机载风能系统上对这些结果的验证。在机载风能系统中，传统的塔架被系绳和升降体(机翼或空气调节器)所取代，后者将水平轴涡轮机提升到较高的高度。由于系绳长度可以调整，因此可以改变工作高度，以最佳地利用风力资源。这项工作将包括一个重要的互补性教育部分，其中研究生、本科生和STEM高中生将利用NREL的多能源混合优化模型(HOMER)软件来优化北卡罗来纳州和加利福尼亚州微电网的可再生/存储/可调度网络配置。这项研究将为在时空变化和部分可观察的环境中运行的系统获得新的控制理论知识和工具。虽然时变环境中的最优控制是一个可以通过马尔可夫模型解决的研究得很好的问题，但空间分量的增加导致状态数量的爆炸性增长，使得基于马尔可夫的方法在大多数情况下在计算上是不可行的。此外，部分可观测性的存在导致了探索(获得空间环境知识)和开发(在最有利的位置进行操作)之间的基本权衡。为了解决这一时空优化问题的复杂性，本研究将探索使用多速率、多尺度的分层框架。具体地说，上层控制器将在非常粗略的网格上执行全局优化(从而使优化在计算上易于处理)，而下层优化将在更精细的网格上执行调整。研究将重点放在模型预测控制的上层优化上，并将探索极值搜索和模型预测控制策略在下层的使用。控制算法将在一个比空气轻的机载风能系统模型上进行验证，使用真实的风切变剖面模型和负载需求数据。在这个机载风能系统中，风速只能在系统的S工作高度上测量到(从而使问题部分可见)，通过对工作高度的优化调整可以实现显著的发电量改善，通过工作高度的优化调整可以实现结构的改善。

The objective of this research is to pioneer new control strategies for emerging systems whose operating environments change as functions of both time and a controllable spatial position. Such applications include coordinated unmanned aerial vehicles that operate in variable atmospheric conditions, concepts for relocatable marine hydrokinetic energy systems that operate in a varying ocean environment, and airborne wind energy systems that operate in an atmospheric environment where the wind varies with respect to both time and vertical position. This research will focus on deriving general theory that will be relevant to a variety of applications, along with the validation of these results on an airborne wind energy system. In airborne wind energy systems, the conventional tower is replaced by tethers and a lifting body (a wing or aerostat) that elevates a horizontal-axis turbine to high altitudes. Because the tether lengths can be adjusted, the operating altitude can be varied to optimally harness the wind resource. The work will include a substantial complementary educational component, wherein graduate, undergraduate, and STEM high school students will utilize NREL's Hybrid Optimization Model for Multiple Energy Resources (HOMER) software to optimize renewable/storage/dispatchable network configurations for microgrids in North Carolina and California.This research will derive new control theoretic knowledge and tools for the systems that operate in a spatiotemporally varying and partially observable environment. While optimal control in a temporally varying environment is a well-studied problem that can be addressed through Markov models, the addition of a spatial component results in an explosion in the number of states, rendering Markov-based methods computationally infeasible in most cases. Furthermore, the presence of partial observability results in a fundamental tradeoff between exploration (obtaining knowledge of the spatial environment) and exploitation (operating at the most favorable locations). To address the complexities of this spatiotemporal optimization problem, this research will explore the use of a multi-rate, multi-scale hierarchical framework. Specifically, an upper-level controller will perform a global optimization over a very coarse grid (thereby rendering the optimization computationally tractable), and a lower-level optimization will perform adjustments on a much finer grid. The research will focus on model predictive control for the upper-level optimization and will explore the use of extremum seeking and model predictive control strategies at the lower level. Control algorithms will be validated on a model of a lighter-than-air airborne wind energy system, using real wind shear profile models and load demand data. In this airborne wind energy system, the wind speed is only measurable at the system?s operating altitude (thereby making the problem partially observable), and significant energy production improvements can be realized through the optimal adjustment of the operating altitude.uction improvements can be realized through the optimal adjustment of the operating altitude.