New SOS method formally verifies stability for saturated INDI aircraft control

Incremental nonlinear dynamic inversion (INDI) is a widely used flight control method valued for its robustness against disturbances. However, formally verifying its stability has traditionally relied on linearized dynamical models, which lose accuracy under actuator saturation and nonlinear operating conditions. This new paper from Dalim Wahby, Lorenzo Schenk, and Guillaume Ducard tackles that gap by representing the saturated INDI controller as an equivalent recurrent equilibrium network (REN). This transformation exactly maps the closed-loop dynamics to an augmented state-feedback system, enabling the use of sum-of-squares (SOS) programming to synthesize a locally valid Lyapunov function without conservative bounding approximations.

Applying this approach to the pitch-rate dynamics of a hybrid vertical take-off and landing (VTOL) aircraft, the authors compute an inner estimate of the region of attraction (RoA)—the set of states from which the controller can recover stability. Crucially, this RoA accounts for actuator saturation, formally verifying stability in regimes where linear margins fail. The method provides a rigorous nonlinear stability certificate, paving the way for safer flight control systems in emerging urban air mobility and other autonomous aircraft applications.