Sensitivity analysis of optimal control motivated by model predictive control

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Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Sensitivity analysis of optimal control motivated by model predictive control.
In: Proceedings of the 23rd International Symposium on Mathematical Theory of Networks and Systems. - Hong Kong , 2018 . - S. 93-96

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Abstract

We analyze the sensitivity of the extremal equations that arise when concluding first order optimality conditions for time dependent optimization problems. More specifically, we consider parabolic PDEs with a linear quadratic performance criterion. We prove the solutions boundedness with respect to the right-hand side of the first order optimality condition which includes initial data. As a consequence, it can be shown that the influence of a perturbation at at certain time decays exponentially in the temporal distance to the time of perturbation. Moreover, a quantitative turnpike theorem can be derived.