A Novel Method for Flight Control Laws Robustness Analysis Over Unsteady Trajectories

A hybrid approach to robustness analyses of flight control laws in re-entry applications

“…In the following, we briefly recall the robustness analysis problem setting and the practical stability criterion. For a more detailed description, the interested reader is referred to [5]. In order to provide a flight dynamics description suitable to winged vehicles performing an atmospheric re-entry, let us consider the following dynamical system:…”

“…In [13], the linear system is considered a valid approximation within a norm-ball, whose radius is fixed by heuristics depending on the linear trajectory characteristics. In [5], the approximation error over a polytope in the parameters space is estimated by its maximum value over the polytope's vertices, assuming that the polytope is sufficiently smaller than the scale at which the system exhibits significant nonlinear behavior so that the maximum error always occurs in a vertex. In the present paper, we propose to evaluate the approximation error by probabilistic methods.…”

“…Indeed, examples of their application in cases of practical interest within the robustness analysis context are quite scarce. In a previous work by the authors [5], this robustness analysis problem was approached by combining practical stability analysis methods for Linear Time Varying (LTV) systems with an approximate description of the original nonlinear system by a certain number of its time-varying linearizations. However, determination of which time-varying linearizations were appropriate for approximating the nonlinear system was found to be an intractable problem, and the approximation was thus performed heuristically.…”