Energy-optimal control of a particle in a dielectrophoretic system

Dielectrophoresis (henceforth called as DEP) is an electrokinetics-based phenomenon, that involves the motion of a particle due to interaction between its dipole moment and a nonuniform electric field around it. This technique is very effective in particle manipulation and separation. Here we consider the control problem involved in moving a particle in the DEP system, from one specified location to another desired location. The voltage on the electrodes which generates the electric field, is the controlling parameter. Optimal control of the motion of a particle is a relevant engineering problem. The time-optimal version of this problem has already been discussed in the literature. The energy-optimal problem for the same system is attempted here. This effort involves a case-wise analysis of the necessary conditions on existence of optimal trajectories, obtained after applying Pontryagin's Maximum principle. An algorithm which would be useful to find an energy-optimal extremal and to simulate the same, is presented.