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

对于许多动态系统，最优周期运行提供了比最佳恒定输入更优越的性能。例如，与静止飞行相比，机载风能系统可以实现更高的表观风速，并通过圆形或8字形轨道飞行产生显著更多的电力。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。应用于机载风能系统，能够以可靠的高速和中等空气密度获得风流，比固定系统更高效、更可靠地发电，从而通过更低的电力成本和更好的能源安全造福社会。此外，该项目将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计划。已有的周期最优控制研究成果主要集中在离线优化方面。人们对以下基本挑战知之甚少：(I)适应未知的植物动态，(Ii)以稳健和稳定的方式实现周期最优，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，从而为稳健的在线周期控制提供了一个新的框架。在存在参数不确定性的情况下，将寻求两种不同的方法来在线优化周期控制轨迹，即一种新的极值搜索方法的实现，以及一种间接自适应控制算法。利用弗洛奎特理论对闭环系统的稳定性进行分析。性能将在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.