Abstract
The nonlinear control problem of aircraft trajectory tracking is tackled in the framework of multiple linear time-varying constrained control using the newly developed paradigm of generalised dynamic inversion. The time differential forms of the multiple constraints encapsulate the control objectives, and are inverted to obtain the reference trajectory-realising control law. The inversion process utilises the Moore-Penrose generalised inverse and the associated nullspace projection, and it predictably involves the problematic generalised inversion singularity. Thus, a singularity avoidance scheme based on a new type of dynamically scaled generalised inverses is introduced that guarantees both 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 by the particular part of the control law on the range space of the transposed constraint matrix, and it works to impose the prescribed aircraft constrained dynamics. The other control action is performed by the auxiliary part of the control law on the complementary orthogonal nullspace of the constraint matrix, and it provides aircraft's global inner stability using the concept of perturbed feedback linearisation. Numerical simulations of an aggressive multiaxial aircraft coordinated manoeuvre verify the efficacy of designing nonlinear flight control systems via this methodology.