  This paper presents a novel, Fourier series based numerical method of
open-loop control optimization. Due to its flexible assumptions, it can be
applied in a large variety of systems, including discontinuous ones or even
so-called black boxes, whose equations are not fully known. This aspect is
particularly important in mechanical systems, where friction or impact induced
discontinuities are common. The paper includes a mathematical background of the
new method, a detailed discussion of the algorithm and a numerical example, in
which control function of a discontinuous capsule drive is optimized. It is
expected that the proposed method can facilitate research in all areas where
control of non-smooth, discontinuous or black box systems is crucial. In
particular, authors hope that the presented algorithm is going to be used for
control optimization of other capsule drives.
