No-regret control of an ill-posed parabolic semilinear equation with an exponential nonlinearity.
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Keywords:
ill-posed problem, regularization, adapted low-regret control, low-regret control, no-regret controlAbstract
Our study focuses on the optimal control of a semilinear parabolic equation featuring incomplete data and an exponential nonlinearity that may blow up in finite time. Based on the principles of no-regret control, low-regret control, and adapted low-regret control, our objective is to define the control strategy for this ill-posed problem. The ill-posed nature of the system makes formulating the optimal control directly challenging. To address this, we use a regularisation approach that incorporates incomplete information. This yields a singular optimality system that characterises the no-regret control for the original semilinear parabolic problem.
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