Optimal control problems without terminal constraints: The turnpike property with interior decay

• Autorzy: Gugat Martin , Lazar Martin

Identyfikatory

DOI

10.34768/amcs-2023-0031

• Języki publikacji: EN

Abstrakty

EN

We show a turnpike result for problems of optimal control with possibly nonlinear systems as well as pointwise-in-time state and control constraints. The objective functional is of integral type and contains a tracking term which penalizes the distance to a desired steady state. In the optimal control problem, only the initial state is prescribed. We assume that a cheap control condition holds that yields a bound for the optimal value of our optimal control problem in terms of the initial data. We show that the solutions to the optimal control problems on the time intervals [0, T] have a turnpike structure in the following sense: For large T the contribution to the objective functional that comes from the subinterval [T/2, T], i.e., from the second half of the time interval [0, T], is at most of the order 1/T. More generally, the result holds for subintervals of the form [r T,T], where r ∈ (0, 1/2) is a real number. Using this result inductively implies that the decay of the integral on such a subinterval in the objective function is faster than the reciprocal value of a power series in T with positive coefficients. Accordingly, the contribution to the objective value from the final part of the time interval decays rapidly with a growing time horizon. At the end of the paper we present examples for optimal control problems where our results are applicable.

Słowa kluczowe

EN

optimal control; turnpike property; system with hyperbolic PDEs; interior decay

PL

sterowanie optymalne; układ hiperboliczny; rozkład wewnętrzny

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2023
• Tom: Vol. 33, no. 3
• Strony: 429--438
• Opis fizyczny: Bibliogr. 25 poz., wykr.

Twórcy

autor

Gugat Martin

• Department of Mathematics, University of Erlangen-Nuremberg, Cauerstr. 11, 91058 Erlangen, Germany

autor

Lazar Martin

• Department of Electrical Engineering and Computing, University of Dubrovnik, Ćira Carića 4, 20 000 Dubrovnik, Croatia

Bibliografia

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