Abstract
The application of model-based optimization methods has become indispensable in science and engineering. Since all models contain systematic errors, the result of optimization can be very sensitive to such errors and even useless. Therefore, application of mathematical optimization to real-life processes demands taking into account uncertainties. One of the remedies is Nonlinear Model Predictive Control (NMPC), which is based on two steps: a simultaneous on-line estimation of the system state and parameters (Moving Horizon Estimation, MHE) and re-optimization of the optimal control for the current parameter and state values (NMPC). The challenge is to solve these optimal control problems with high frequency in real time. During the last decade significant progress has been made in development of so-called multilevel real-time iterations for NMPC for ODE and DAE models to reduce the response time to a few milliseconds compared with standard methods. However, today’s state-of-the-art is to perform MHE and NMPC separately. A next logical step is the development of a simultaneous MHE and NMPC in one step. Another challenge is to transfer recent advances of NMPC to a much more complex case of nonstationary PDE models.
In this paper we present combined multilevel real-time iterations based on coupling of the MHE and NMPC for nonstationary PDE models. These are the first steps towards real time feasibility of the NMPC technique for PDE models.
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This work was supported by the BMBF through the programme “Mathematics for Innovation in Industry and Services”.
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Kostina, E., Kriwet, G. (2018). Multilevel Iterations for the Combined Moving Horizon Estimation and Nonlinear Model Predictive Control for PDE Models. In: Schulz, V., Seck, D. (eds) Shape Optimization, Homogenization and Optimal Control . International Series of Numerical Mathematics, vol 169. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-90469-6_6
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