SOS-based Stability Verification for Saturated INDI Control of Hybrid-VTOL Aircraft Pitch Rate Dynamics

Abstract

Incremental nonlinear dynamic inversion (INDI) is a prominent flight-control strategy valued for its robust disturbance rejection; however, its formal stability verification has traditionally been limited to linearized dynamical models. This paper presents a formal nonlinear stability certificate for a saturated INDI pitch-rate controller for a hybrid vertical take-off and landing (VTOL) aircraft by representing the INDI controller via an equivalent recurrent equilibrium network (REN). By casting the saturated INDI architecture as a REN, the closed-loop dynamics are exactly mapped to an augmented state-feedback system. This structural equivalence enables the use of sum of squares (SOS) programming to synthesize a locally valid Lyapunov function without relying on conservative bounding approximations. The resulting certificate yields an inner estimate of the region of attraction (RoA) that explicitly accounts for actuator saturation, formally verifying the controller's stability in operating regimes where standard linear margins lose their validity.