Collaborative Research: Self-Adjusting Periodic Optimal Control with Application to Energy-Harvesting Flight

对于许多动态系统，最优周期操作提供了比最佳恒输入更好的性能。例如，与静止飞行相比，空中风能系统可以通过圆形或数字8轨道飞行获得更高的表观风速，并产生更多的电力。然而，这些结果可能对不确定性很敏感。例如，当风速变化时，为特定飞行条件设计的周期性能量收集轨迹的性能可能会迅速下降。因此，该项目的总体目标是使动态控制器能够快速调整其周期性操作，以便在不断变化的条件下继续提供近乎最佳的性能。应用于机载风能系统，它可以获得可靠的高速度和中等空气密度的风流，比固定系统更有效、更可靠地发电，从而通过降低电力成本和提高能源安全性来造福社会。此外，在这个项目中创建的基本工具将适用于许多其他重要问题，包括慢性疾病治疗的复发性给药计划。现有的周期最优控制研究主要集中在离线优化方面。对以下基本挑战知之甚少：(i)适应未知的植物动力学，（ii）以鲁棒和稳定的方式实现周期最优性，以及（iii）同时优化周期轨迹的时间周期和形状。该项目解决了这些挑战，从而为鲁棒在线周期性控制提供了一个新的框架。在存在参数不确定性的情况下，将采用两种不同的方法对周期性控制轨迹进行在线优化，即极值寻求方法的新实现和间接自适应控制算法。利用Floquet理论分析闭环系统的稳定性。性能将在模拟基准药物输送问题和能量收集飞行问题中进行评估。最后，通过实验验证了能量收集飞行控制的有效性。

For many dynamic systems, optimal periodic operation provides superior performance to the best possible constant input. For example, compared to stationary flight, airborne wind energy systems can achieve higher apparent wind speed -- and generate significantly more electricity -- by flying in circular or figure-8 orbits. However these results may be sensitive to uncertainty. For example, the performance of a periodic energy harvesting trajectory designed for a particular flight condition may degrade rapidly when wind speed changes. Thus the overarching goal of this project is to enable dynamic controllers that rapidly adjust their periodic operation, in order to continue to provide near-optimal performance despite changing conditions. The application to airborne wind energy systems, which can access wind streams with reliably high speeds and moderate air density, generate electricity more efficiently and more reliably than stationary systems, thus benefiting society through lower power costs and improved energy security. Moreover, the fundamental tools to be created in this project will be applicable to many other important problems, including recurrent drug-delivery scheduling for chronic disease treatment. Existing results on periodic optimal control focus on offline optimization. Very little is known about the following fundamental challenges: (i) adaptation to unknown plant dynamics, (ii) achievement of periodic optimality in a robust and stable manner, and (iii) simultaneous optimization of both the time period and shape of the periodic trajectory. This project addresses these challenges, thereby furnishing a novel framework for robust online periodic control. Two distinct approaches will be pursued for online optimization of periodic control trajectories in the presence of parametric uncertainties, namely a novel implementation of extremum-seeking methods, and an indirect adaptive control algorithm. The closed-loop system stability will be analyzed using Floquet theory. Performance will be evaluated in simulations of a benchmark drug delivery problem and an energy-harvesting flight problem. Finally, effectiveness for control of energy harvesting flight will be validated experimentally.