# Time-optimal control of a particle in a dielectrophoretic system

07 06 Category : Optimal Control | All

**Authors**: Dong Eui Chang, Nicolas Petit, et Pierre Rouchon, IEEE Tr. Automatic Control. Vol. 51, No. 7, pp 1100-1114. 2006, DOI: 10.1109/TAC.2006.878748

We study the time-optimal control of a particle in a dielectrophoretic system. This system consists of a time-varying nonuniform electric ﬁeld which acts upon the particle by creating a dipole within it. The interaction between the induced dipole and the electric ﬁeld generates the motion of the particle. The control is the voltage on the electrodes which induces the electric ﬁeld. Since we are considering the motion of a particle on an invariant line in a chamber ﬁlled with ﬂuid ﬂowing at low Reynolds number, the dynamics have a two dimensional state; one for the particle position and the other for the induced dipole moment. In regard to time-optimal control, we address the issue of existence and uniqueness of optimal trajectories, and explicitly compute the optimal control and the corresponding minimum time. Finally, we cast our analysis in the framework of symplectic reduction theory in order to provide geometric insight into the problem.

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BibTeX:

@Article{,

author = {Nicolas Petit Dong Eui Chang, Pierre Rouchon},

title = {Time-optimal control of a particle in a dielectrophoretic system},

journal = {IEEE Transactions on Automatic Control.},

volume = {51},

number = {7},

pages = {1100-1114},

year = {2006},

}