Evolutionary optimisation of Hénon map control: a black box approach

This paper deals with the usage of heuristics for the optimisation of the control of chaotic system. The main aim of this paper is to show a new approach of solving this problem and constructing new cost functions (CFs) operating in 'black box mode' without a previous exact mathematical analysis of the system, thus without knowledge of the stabilising target state. Three proposals of 'black box' mode CFs were tested in this paper. As a model of deterministic chaotic system, the two‐dimensional Hénon map was used. The optimisations were realised in several ways, each one for another desired state of system. Evolutionary algorithms (EAs) self‐organising migrating algorithm and differential evolution were used. For each version, repeated simulations were conducted to outline the effectiveness and robustness of the used method and CF.