High-order fully actuated system approaches: Model predictive control with applications to under-actuated systems

The main results of this paper are concentrated on the nonlinear model predictive control (MPC) tracking optimization based on high-order fully actuated (HOFA) system approaches. The proposed HOFA MPC strategy makes full use of full-actuation property to eliminate the nonlinear dynamics of the system, and then the nonlinear optimization problem is equivalently transformed into a series of easy-solve linear convex optimization problems. Different from general nonlinear MPC methods and the current optimal control of the HOFA system approach, an analytical controller with smooth and less energy is obtained by the moving horizon optimization. And it is proven that the proposed controller can stabilize the corresponding tracking error closed-loop system. Finally, not limited to FA systems, as examples, a nonlinear numerical under-actuated model in the mathematical sense and a benchmark nonlinear under-actuated mechanical system are transformed into corresponding equivalent HOFA systems, the simulation results are given to verify the effectiveness of the proposed strategy.