Naslov
The turnpike property with interior decay for optimal control problems

Autori
Gugat, Martin ; Lazar, Martin

Vrsta, podvrsta
Radovi u časopisima, znanstveni

Izvornik
International Journal of Applied Mathematics and Computer Science (2022)

Status rada
Prihvaćen

Ključne riječi
Optimal control, turnpike property, system with hyperbolic PDEs, interior decay

Sažetak
We show a turnpike result for problems of optimal control with possibly nonlinear systems and 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 of 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 this subinterval in the objective function is faster than the reciprocal value of a power series in T with positive coefficients. At the end of the paper we present optimal control problems where our results are applicable.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA