TY - JOUR

T1 - LINEAR PROGRAMMING ESTIMATES FOR CESÀRO AND ABEL LIMITS OF OPTIMAL VALUES IN OPTIMAL CONTROL PROBLEMS

AU - Gaitsgory, Vladimir

AU - Shvartsman, Ilya

N1 - Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.

PY - 2022/3

Y1 - 2022/3

N2 - We consider infinite horizon optimal control problems with time averaging and time discounting criteria and give estimates for the Cesàro and Abel limits of their optimal values in the case when they depend on the initial conditions. We establish that these limits are bounded from above by the optimal value of a certain infinite dimensional (ID) linear programming (LP) problem and that they are bounded from below by the optimal value of the corresponding dual problem. (These estimates imply, in particular, that the Cesàro and Abel limits exist and are equal to each other if there is no duality gap). In addition, we obtain IDLP-based optimality conditions for the long run average optimal control problem, and we illustrate these conditions by an example.

AB - We consider infinite horizon optimal control problems with time averaging and time discounting criteria and give estimates for the Cesàro and Abel limits of their optimal values in the case when they depend on the initial conditions. We establish that these limits are bounded from above by the optimal value of a certain infinite dimensional (ID) linear programming (LP) problem and that they are bounded from below by the optimal value of the corresponding dual problem. (These estimates imply, in particular, that the Cesàro and Abel limits exist and are equal to each other if there is no duality gap). In addition, we obtain IDLP-based optimality conditions for the long run average optimal control problem, and we illustrate these conditions by an example.

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U2 - 10.3934/dcdsb.2021102

DO - 10.3934/dcdsb.2021102

M3 - Article

AN - SCOPUS:85112042497

SN - 1531-3492

VL - 27

SP - 1591

EP - 1610

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 3

ER -