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Some examples of applications in deterministic optimal control

First example is the energy management problem for a microgrid system including a diesel generator and a photovoltaic plant with a battery storage system. The aim is to satisfy the power demand while minimizing the total operational cost. This cost is primarily the diesel consumption but also includes the replacement cost of the battery system, whose aging has to be estimated. A second example is a study of locomotion in a fluid with low Reynolds number, more precisely the so-called 3-link or Purcell micro-swimmer. We are interested in optimizing both the swimming strategy (stroke) and the swimmer design (link ratio) for maximal displacement. Resistive Force Theory is used to reformulate the swimmer’s dynamics as an ODE suitable for optimization. Third example is set in medical imaging, namely the contrast problem in Magnetic Nuclear Resonance. Here we seek the magnetic field to be applied in order to obtain the best constrast, which can be formulated as a optimal control problem on spin particles. Specific difficulties are the presence of bang/singular arcs as well as the spatial inhomogeneities in the magnetic field.

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