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Distributed and boundary model predictive control for the heat equation. (English) Zbl 1256.49033

Summary: We consider a Model Predictive Control (MPC) scheme without stabilizing terminal constraints applied to the linear heat equation. We apply a method to analyze minimal stabilizing optimization horizons based on an exponential controllability condition. While the method is known to yield conservative quantitative results for concrete examples, our analysis shows that it precisely determines qualitative changes in the horizon for changing parameters and changing problem structures. Particularly, it is able to explain numerically observed differences in the stability behavior of MPC for distributed and for boundary control.

MSC:

49M25 Discrete approximations in optimal control
49K20 Optimality conditions for problems involving partial differential equations
35K05 Heat equation
93B05 Controllability
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