Abstract
This paper gives an extension of previous work on gradient optimal control of distributed parabolic systems to the case of distributed bilinear systems which are a type of nonlinear systems. We introduce the notion of flux optimal control of distributed bilinear systems. The idea is trying to achieve a neighborhood of the gradient state of the considered system by minimizing a nonlinear quadratic cost. Using optimization techniques, a method showing how to reach a desired flux at a final time, only on internal subregion of the system domain will be proposed. The proposed simulation illustrates the theoretical approach by commanding the heat bilinear equation flux to a desired profile.
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