In backstepping implementation, the derivatives of virtual control signals are required at each step. This study provides a novel way to solve this problem by combining
online optimisation with backstepping design in an outer and inner loop manner. The
properties of differential flatness and the B-spline polynomial function are exploited
to transform the optimal control problem into a computationally efficient form. The
optimisation process generates not only the optimised states but also their finite order
derivatives which can be used to analytically calculate the derivatives of virtual control signal required in backstepping design. In addition, the online optimisation repeatedly performed in a receding horizon fashion can also realise local motion planning for obstacle avoidance. The stability of the receding horizon control scheme is analysed via
Lyapunov method which is guaranteed by adding a parametrised terminal condition in the online optimisation. Numerical simulations and flight experiments of a quadrotor unmanned air vehicle are given to demonstrate the effectiveness of the proposed composite control method
