Soft-landing control by control invariance and receding horizon control

We propose a design for soft landing control based on control invariant sets and receding horizon control. Soft landing control, which is of interest in several applications in aerospace, transportation systems, and factory automation, aims at achieving precise positioning of a moving object to a target position, while ensuring that the maximum velocity decreases as the target is approached. The resulting soft contact avoids damages and wear. In this paper, we formulate appropriate constraints and recast soft landing control as the generation of an admissible trajectory of the constrained system. Then, we compute a control invariant set and design a receding horizon control law that forces the state to remain in such set. Thus, the trajectories generated by the controller achieve soft landing, regardless of the controller cost function and horizon, also when the dynamics are uncertain. We demonstrate our approach by a case study in transportation systems.