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

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.