Nonlinear control allocation for non-minimum phase systems

In this brief, we propose a control allocation method for a particular class of uncertain over-actuated affine nonlinear systems, with unstable internal dynamics. Dynamic inversion technique is used for the commanded output to track a smooth output reference trajectory. The corresponding control allocation law has to guarantee the boundedness of the states, including the internal dynamics, and satisfy control constraints. The proposed method is based on a Lyapunov design approach with finite-time convergence to a given invariant set. The derived control allocation is in the form of a dynamic update law which, together with a sliding mode control law, guarantees boundedness of the output tracking error as well as of the internal dynamics. The effectiveness of the control law is tested on a numerical model of the non-minimum phase planar vertical take-off and landing (PVTOL) system.