Optimal Control for Parabolic Uncertain System Based on Wavelet Transformation

In this paper, we study a new type of optimal control problem subject to a parabolic uncertain partial differential equation where the expected value criterion is adopted in the objective function. The basic idea of Haar wavelet transformation is to transform the proposed problem into an approximate uncertain optimal control problem with arbitrary accuracy because the dimension of Haar basis tends to infinity. The relative convergence theorem is proved. An application to an optimal control problem with an uncertain heat equation is dealt with to illustrate the efficiency of the proposed method.

Automated summary

This paper investigates a new type of optimal control problem involving a parabolic uncertain partial differential equation, where the objective function adopts an expected value criterion. The fundamental idea of Haar wavelet transformation is to approximate the proposed problem with arbitrary accuracy by converting it into an uncertain optimal control problem due to the infinitely increasing dimensions of Haar basis. The relative convergence theorem is proven, and an application to an optimal control problem with an uncertain heat equation is presented to demonstrate the effectiveness of the proposed method.