Interpolation Based Control for reference tracking under constraints

This article introduces an adaptation of the Interpolation Based Control (IBC) technique developed recently for the constraint regulation. The aim of this work is to address the particularities of the trajectory tracking control problems in the presence of constraints. In this framework, the main challenge comes from translation of the constraint set as a result of the evolution of the trajectory to be tracked. Even if the trajectory satisfies the dynamical constraints, and those dynamics are linear, the translation of the constraints set leads to changes in the controllable regions. The main idea in the present contribution is to adapt IBC's ingredients to the trajectory tracking by constructing a virtual feasible trajectory with particular properties and enable the interpolation on scalable version of the controlled invariant sets designed initially for regulation. As a secondary objective, the analysis the shape of the real trajectory and the computational burden points to the possible parametrization of the virtual trajectory and enhance the proposed methodology.