Aircraft maneuvering control using generalized dynamic inversion and semidefinite Lyapunov functions

The generalized dynamic inversion paradigm is applied to aircraft maneuvering control design. A partially nonlinear aircraft model is decomposed into outer and inner subsystems. A scalar outer subsystem deviation function is defined, and a linear stable dynamics in this deviation function is manipulated to obtain a linear equation in the control vector. The equation is inverted using the Greville formula, resulting in the control law. The particular part of the control law drives the outer subsystem states to their desired values, and the auxiliary part acts to stabilize the vehicle´s internal dynamics by means of the null-control vector. The null-control vector is constructed via a class of novel positive semidefinite Lyapunov functions and nullprojected Lyapunov equations. The performance of the aforementioned control system is evaluated by comparing with the performance of an optimal linear quadratic regulator as applied to the same partially nonlinear system. Numerical simulations show the stability and performance characteristics of the two closed loop systems to be comparable, demonstrating the efficacy of the proposed generalized dynamic inversion control law.