Abstract
In this paper we use a reference trajectory computed by a model predictive method to shrink the computational domain where we set the Hamilton-Jacobi Bellman (HJB) equation. Via a reduced-order approach based on proper orthogonal decomposition(POD), this procedure allows for an efficient computation of feedback laws for systems driven by parabolic equations. Some numerical examples illustrate the successful realization of the proposed strategy.
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Acknowledgements
G. Fabrini gratefully acknowledges support by the German Science Fund DFG grant Reduced-Order Methods for Nonlinear Model Predictive Control.
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Fabrini, G., Falcone, M., Volkwein, S. (2019). Coupling MPC and HJB for the Computation of POD-Based Feedback Laws. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_89
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DOI: https://doi.org/10.1007/978-3-319-96415-7_89
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