Pre-Stabilized Energy-Optimal Model Predictive Control

This paper presents Pre-stabilized Energy-optimal Model Predictive Control which is developed based on the existing Energy-Optimal Model Predictive Control (EOMPC) approach. EOMPC is a control method to realize energyoptimal point-to-point motions within a required motion time. In order to obtain a sufficiently large prediction time horizon with a limited number of decision variables resulting in less computational load and solving the optimization problem within the chosen sampling time, nonequidistant time intervals are used over the prediction horizon. This approach is called blocking. However blocking yields a non-smooth optimal solution and as a result the energy-optimality is only approximately achieved. In order to overcome this drawback, this paper proposes a prestabilization strategy to reduce the computational load of EOMPC. Pre-stabilization uses deadbeat state feedback to modify the system models employed in the formulation of MPC and yields a much sparser optimization problem. The significant advantage of the pre-stabilization on computational speed of MPC optimization problems is clarified. The computational efficiency and performance of EOMPC with pre-stabilization is validated through numerical simulations.