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

TL;DR

This paper introduces a Fourier series based numerical method for open-loop control optimization, capable of handling discontinuous and black box systems, demonstrated through a capsule drive example.

Contribution

It presents a new flexible Fourier series based optimization method applicable to discontinuous and black box systems, expanding control optimization capabilities.

Findings

Method successfully optimized control of a discontinuous capsule drive

Applicable to systems with unknown or discontinuous dynamics

Potential to advance control research in non-smooth systems

Abstract

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.