Generalized Dynamic Inversion for Multiaxial Nonlinear Flight Control

The nonlinear problem of aircraft trajectory tracking is tackled in the framework of multiple linear time-varying constrained control using the newly developed paradigm of generalized dynamic inversion. The time differential forms of the multiple constraints encapsulate the control objectives, and are inverted to obtain the reference trajectory-realizing control law. The inversion process utilizes the Moore-Penrose generalized inverse, and it predictably involves the problematic generalized inversion singularity. Thus, a singularity avoidance scheme based on a new type of dynamic scaling factors is introduced that guarantees asymptotically stable tracking and singularity avoidance. The steady state closed loop system allows for two inherently noninterfering control actions working towards a unified goal to exploit the aircraft's control authority over the entire state space. One control action is performed on the range space of the constraint generalized inverse matrix, and it works to impose the prescribed aircraft constrained dynamics. The other control action is performed on the complementary orthogonal nullspace of the constraint matrix, and it provides aircraft's global inner stability using a novel type of dynamically scaled nullprojection control Lyapunov functions. Numerical simulations of a multiaxial aircraft coordinated maneuver verify the efficacy of designing nonlinear flight control systems via this technique.