Abstract
The increasing ubiquity of complex systems that require control is a challenge for existing methodologies in characterization and controller design when the system is high-dimensional, nonlinear, and without physics-based governing equations. We review standard model reduction techniques such as Proper Orthogonal Decomposition (POD) with Galerkin projection and Balanced POD (BPOD). Further, we discuss the link between these equation-based methods and recently developed equation-free methods such as the Dynamic Mode Decomposition and Koopman operator theory. These data-driven methods can mitigate the challenge of not having a well-characterized set of governing equations. We illustrate that this equation-free approach that is being applied to measurement data from complex systems can be extended to include inputs and control. Three specific research examples are presented that extend current equation-free architectures toward the characterization and control of complex systems. These examples motivate a potentially revolutionary shift in the characterization of complex systems and subsequent design of objective-based controllers for data-driven models.
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Proctor, J.L., Brunton, S.L. & Kutz, J.N. Including inputs and control within equation-free architectures for complex systems. Eur. Phys. J. Spec. Top. 225, 2413–2434 (2016). https://doi.org/10.1140/epjst/e2016-60057-9
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DOI: https://doi.org/10.1140/epjst/e2016-60057-9