Worst-Case Disturbances for Time-Varying Systems with Application to Flexible Aircraft

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.