This paper presents "optimal identification," a framework for using experimental data to identify the optimality conditions associated with the feedback control law implemented in the measurements. The technique compares closed loop trajectory measurements against a reduced order model of the open loop dynamics, and uses linear matrix inequalities to solve an inverse optimal control problem as a convex optimization that estimates the controller optimality conditions. In this study, the optimal identification technique is applied to two examples, that of a millimeter-scale micro-quadrotor with an engineered controller on board, and the example of a population of freely flying Drosophila hydei maneuvering about forward flight. The micro-quadrotor results show that the performance indices used to design an optimal flight control law for a micro-quadrotor may be recovered from the closed loop simulated flight trajectories, and the Drosophila results indicate that the combined effect of the insect longitudinal flight control sensing and feedback acts principally to regulate pitch rate.

Commercially available speed controllers, motors, and propellers typically comprise the powertrains of many micro aerial robotic systems, such as quadrotor vehicles. As on board state sensing and processing improves, actuation bandwidth is becoming a significant bottleneck that limits the performance of the entire closed loop system. The performance of the commercial products can be greatly enhanced through the implementation of classical control methods directly at the powertrain level. In this paper, reduced order open loop models for three representative commercially available powertrains were estimated and were compared with closed loop equivalents. Further performance improvement is realized by the addition of a static inverse to mitigate the steady state structured uncertainty of the system.

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