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                <term xml:lang="en">therapeutic magnetic microbeads</term>
                <term xml:lang="en">trajectory constraints</term>
                <term xml:lang="en">velocity constraints</term>
                <term xml:lang="en">Controllability</term>
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                <term xml:lang="en">Saturation magnetization</term>
                <term xml:lang="en">observability conditions</term>
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                <term xml:lang="en">microfluidic channels</term>
                <term xml:lang="en">magnetic gradient fields</term>
                <term xml:lang="en">linear quadratic with integral action control</term>
                <term xml:lang="en">laminar viscous fluidic environment</term>
                <term xml:lang="en">drug targeting applications</term>
                <term xml:lang="en">controllability conditions</term>
                <term xml:lang="en">LQI</term>
                <term xml:lang="en">optimal control</term>
                <term xml:lang="en">observability</term>
                <term xml:lang="en">Magnetic resonance imaging</term>
                <term xml:lang="en">Magnetic separation</term>
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              <p>This paper presents an optimal control strategy for navigation of multiple magnetic microbeads for future drug targeting applications. To transport the drugs, we use therapeutic magnetic microbeads as navigable agents controlled by magnetic gradients. The main difficulty is to control independently each therapeutic agent along a trajectory with the same magnetic gradient fields. This study proposes an optimal control methodology to control a group of different therapeutic agents at desired states. Based on a dynamic model of group of magnetic microbeads, controllability and observability conditions are formulated and simulated. Based on the proposed theoretical analysis a linear quadratic with integral action control (LQI) has been chosen to be applied to the microbeads system. Finally, an experimental investigation is carried out in millimeter-sized fluidic artery vessels to demonstrate the controllability and stability of two magnetic microbeads under different velocity and trajectory constraints with a laminar viscous fluidic environment.</p>
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