Numerical Verification of Turnpike and Continuity Properties for Time-Varying PDEs

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Abstract

To prove approximate closed loop optimality of economic model predictive control of time varying systems, continuity assumptions for the optimal value function and the turnpike property are sufficient conditions. It can be difficult to prove these assumptions analytically for a given example. In this paper we present a numerical approach that aims to verify the assumptions by simulations for a system involving a convection-diffusion equation with boundary control. The results show that the assumptions are realistic and can be met for practical problems.

Keywords

Turnpike Property
Optimal Value Function
Modulus of Continuity
Model Predictive Control
Time-varying systems
Partial Differential Equations

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This research was supported by DFG-Grant GR 1569/16-1.

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