Precision Trajectory Tracking of Magnetically Actuated Microparticles Using Permanent-Magnet Systems Under State Constraints

Magnetically actuated microparticles are promising candidates for minimally invasive microrobotics and targeted delivery in confined microenvironments. Their precise navigation remains challenging because viscous drag, flow disturbances, and safety constraints can prevent accurate trajectory tracking. This paper investigates precision tracking of magnetic microparticles actuated by permanent-magnet systems under state constraints and bounded disturbances. The control problem is formulated at the magnetic-force level, where the force applied to the microparticle is treated as the controlled input. This formulation is motivated by permanent-magnet actuation architectures while remaining applicable when the desired magnetic force can be generated or approximated. An invariant-set-based disturbance rejection strategy is developed. First, an optimized linear controller is obtained using linear matrix inequalities (LMIs) to minimize the output invariant ellipsoid while satisfying state constraints. Then, a homogeneous controller is introduced to improve convergence and tracking accuracy. A worst-case disturbance direction is also characterized. Simulations in a blood-like viscous environment show improved convergence and accuracy with the homogeneous controller, supporting force-level constrained control for precision permanent-magnet actuation of microparticles.