Approximate Modeling of Dynamical Systems Applying HAVOK: A Systematic Review

Systems modeling has played a crucial role in understanding and solving complex real-world problems, some of which can be computationally expensive. To address this issue, surrogate modeling reduces the dimensionality of such problems, enabling less processor-consuming solutions. One method within surrogate modeling is the Hankel alternative view of Koopman (HAVOK) method, which allows the decomposition of chaotic dynamics into a linear model with intermittent forcing. However, the application of this approach in the field of control systems, particularly within the framework of fault-tolerant control systems, still needs to be explored. This paper aims to present a systematic review of the literature on surrogate modeling applied to control systems, focusing on three specific inquiries. First, the study investigates the surrogate modeling methods commonly used in fault detection and diagnosis. Second, it explores the surrogate modeling methods predominantly utilized in describing chaotic phenomena and dynamical systems. Lastly, the paper explores the potential of applying the HAVOK method to control and model system faults. A comprehensive search yielded 75 relevant articles published in the last five years. From this pool, 12 articles were selected for review. The findings revealed that the full implementation of the HAVOK method in control and fault prediction has not yet been realized.