Reset control of the double integrator with finite settling time and finite jerk

Abstract

This work develops a new reset-based feedback controller that stabilizes a double integrator plant, in finite-time under a finite-jerk restriction (that is without jumps in acceleration). It is proved that these objectives can be achieved by a second order controller with adequate jerk resettings and a special crossing manifold. The solution is justified with the help of an intuitive geometrical approach (spherical projection of trajectories). The nominal solution is robustified as a hybrid system and simulations show satisfactory performance under output disturbances and state measurement uncertainty. The proposal is compared to several finite-time controllers previously developed in the literature.