Approximate Optimal Regulator for Distributed Control Problem with Superposition Functional and Rapidly Oscillating Coefficients
In this paper, we consider the optimal stabilization problem on infinite time interval for a parabolic equation with rapidly oscillating coefficients and non-decomposable quadratic cost functional with superposition type operator. In general, to find the exact formula of optimal regulator is not possible for such a problem, because the Fourier method cannot be directly applied. But the transition to the homogenized parameters greatly simplifies the structure of the problem. Assuming that the problem with the homogenized coefficients already admits optimal regulator, we ground approximate optimal control in the feedback form for the initial problem. We give an example of superposition operator for specific conditions in this paper.
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