Abstract
The application of autoencoders in combination with Dynamic Mode Decomposition for control (DMDc) and reduced order observer design as well as Kalman Filter design is discussed for low order state reconstruction of a class of scalar linear diffusion-convection-reaction systems. The general idea and conceptual approaches are developed following recent results on machine-learning based identification of the Koopman operator using autoencoders and DMDc for finite-dimensional discrete-time system identification. The resulting linear reduced order model is combined with a classical Kalman Filter for state reconstruction with minimum error covariance as well as a reduced order observer with very low computational and memory demands. The performance of the two schemes is evaluated and compared in terms of the approximated L2 error norm in a numerical simulation study. It turns out, that for the evaluated case study the reduced-order scheme achieves comparable performance with significantly less computational load.
Highlights
The problem of system state reconstruction from local and partial state measurements has important impacts on the ability of controlling the system state and monitoring system health and performance [1,2,3]
The application of autoencoders in combination with Dynamic Mode Decomposition for control (DMDc) and reduced order observer design as well as Kalman Filter design is discussed for low order state reconstruction of a class of scalar linear diffusion-convection-reaction systems
The resulting linear reduced order model is combined with a classical Kalman Filter for state reconstruction with minimum error covariance as well as a reduced order observer with very low computational and memory demands
Summary
The problem of system state reconstruction from local and partial state measurements has important impacts on the ability of controlling the system state and monitoring system health and performance [1,2,3]. Lumping based on the combination of DMDc with state estimation has already been shown in several application scenarios to yield satisfactory performance [3,17,18,19,20] In these studies the Kalman Filter [21,22] has been used on the basis of the obtained finite-dimensional linear discrete-time model equations. One potential drawback for implementations of the Kalman Filter in real-time applications relies on the fact that it requires n2 + n dynamic variables, where n is the number of states in the reduced-order model, given that the n × n error covariance matrix must be calculated online to provide the optimal filter performance In comparison to this approach, alternative design methods, such as the reduced-order [1,2] or the geometric observer [23].
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