The aim of this Paper is to propose a method for constructing worst-case disturbances to analyze the performance of linear time-varying systems on a finite time horizon. This is primarily motivated by the goal of analyzing flexible aircraft, which are more realistically described as time-varying systems, but the same framework can be applied to other fields in which this feature is relevant. The performance is defined by means of a generic quadratic cost function, and the main result consists of a numerical algorithm to compute the worst-case signal verifying that a given performance objective is not achieved. The developed algorithm employs the solution to a Riccati differential equation associated with the cost function. Theoretically, the signal can also be obtained by simulating the related Hamiltonian dynamics, but this does not represent a numerically reliable strategy, as commented in the Paper. The applicability of the approach is demonstrated with a case study consisting of a flexible aircraft subject to gust during a flight-test maneuver.
Bibliographical noteFunding Information:
This work has received funding from the Horizon 2020 research and innovation programme under grant agreement number 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Control. The authors are thankful for Sérgio Waitman for providing the controller used in the analyses.
© 2018 by the American Institute of Aeronautics and Astronautics, Inc.