A novel, Fourier series based method of control optimization and its application to a discontinuous capsule drive model

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 "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 practical, 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.