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

对于许多动态系统，最佳周期操作提供了比最佳可能恒定输入更优越的上级性能。 例如，与静止飞行相比，空中风能系统可以通过在圆形或8字形轨道上飞行来实现更高的表观风速，并产生更多的电力。 然而，这些结果可能对不确定性敏感。 例如，当风速改变时，为特定飞行条件设计的周期性能量收集轨迹的性能可能迅速降低。 因此，该项目的首要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接近最佳的性能。 应用于空中风能系统，可以可靠地获得高速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造福社会。 此外，该项目中创建的基本工具将适用于许多其他重要问题，包括慢性病治疗的经常性药物输送时间表。现有的周期最优控制研究主要集中在离线优化上。 对以下基本挑战知之甚少：（i）适应未知的植物动态，（ii）以鲁棒和稳定的方式实现周期性最优，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，从而提供了一个新的框架，强大的在线定期控制。两种不同的方法将追求在线优化的周期性控制轨迹的存在参数的不确定性，即一种新的实现极值搜索方法，和一个间接的自适应控制算法。 闭环系统的稳定性将使用Floquet理论进行分析。 性能将在一个基准药物输送问题和能量收集飞行问题的模拟中进行评估。 最后，对能量收集飞行控制的有效性进行了实验验证。

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.