TY - JOUR

T1 - On Average Control Generating Families for Singularly Perturbed Optimal Control Problems with Long Run Average Optimality Criteria

AU - Gaitsgory, Vladimir

AU - Manic, Ludmila

AU - Rossomakhine, Serguei

PY - 2015/3/1

Y1 - 2015/3/1

N2 - The paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional (ID) linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with a numerical example.

AB - The paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional (ID) linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with a numerical example.

KW - Averaging and linear programming

KW - Numerical solution

KW - Occupational measures

KW - Singularly perturbed optimal control problems

UR - http://www.scopus.com/inward/record.url?scp=84958548051&partnerID=8YFLogxK

U2 - 10.1007/s11228-014-0306-3

DO - 10.1007/s11228-014-0306-3

M3 - Article

VL - 23

SP - 87

EP - 131

JO - SET-VALUED ANALYSIS

JF - SET-VALUED ANALYSIS

SN - 0927-6947

IS - 1

ER -