Control of two-magnet system under state and input constraints

This work is concerned with targeted drug delivery inside the human body by using magnetic microrobots and permanent magnets. Due to the constraints of permanent magnet field, the pull and push action on magnetic particle need to be activated in a certain space. In this paper, the stabilization of particle under state and input constraints is studied. The objective is to design an optimized controller under state and input constraint for particle so that it can be stabilized around the desired location. The dynamic model of particle is based on the gravity, magnetic, buoyancy, hydrodynamic and neglects other small forces. The optimized controller is obtained by solving a group of LMIs (Linear matrix inequalities) while minimizing the objective function. LMI system that characterizes the stability and convergences properties of system is built by Lyapunov method and invariant set theorem. The key novelty of this work is that the optimized controller is proven feasible for permanent magnet to stabilize the magnetic particle inside a minimal invariant set.