Including inputs and control within equation-free architectures for complex systems
1 Institute for Disease Modeling, Bellevue, WA 98004, USA
2 Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
3 Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
a e-mail: firstname.lastname@example.org
Received: 19 February 2016
Revised: 28 June 2016
Published online: 22 November 2016
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.
© The Author(s) 2016
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