469307 Equation-Free Control of Distributed Parameter Systems Using Discrete Empirical Interpolation Method and Proper Orthogonal Decomposition
This issue motivates us to propose an approach to control systems when the knowledge of the chemical and physical law that describes the systems is unavailable or incomplete but the effect of actuators is known. First, POD is applied to generate two sets of basis functions that are used to estimate the system dynamics and state. Then discrete empirical interpolation method (DEIM)  is employed to determine the location of sensors. DEIM was proposed to reduce the computational cost associated with the nonlinear term in the reduced order model generated by Galerkin-POD methodology. Because DEIM has the property that the selection of the interpolation indices can limit the growth of the error of the approximation, it is modified to determine sensor location in our method. Compared with other sensor network design methods, this approach does not require the a priori knowledge of the governing equation. Having continuous measurements from these sensors, the state in the ROM is estimated by a static observer. Using a similar approach as the static observer, a mapping from the measurement of the velocity sensors onto the projection of the dynamics is generated. The estimation of the system dynamics and state make the model redundant in controller design.
Compared with other equation free methods, including divide-and-conquer techniques (such as memory based local modeling), subspace identification, neural network, and autoregressive moving average with exogenous inputs (ARMAX), the proposed method is computationally cheaper. The method performance is illustrated on a diffusion reaction process.
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