2014/12/06 by Mathieu Claeys, Didier Henrion, Claeys, Mathieu +3
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.1412.2278
arXiv admin note: text overlap with arXiv:1404.4699
arxiv created 2014/12/06 · arxiv updated 2014/12/20
Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phe-nomena, by relaxing controls as Young measures. These semi-definite relaxations were later on extended to optimal control problems depending linearly on the con-trol input and typically featuring concentration phenomena, interpreting the control as a measure of time with a discrete singular component modeling discontinuities or jumps of the state trajectories. In this contribution, we use measures intro-duced originally by DiPerna and Majda in the partial differential equations litera-ture to model simultaneously, and in a unified framework, possible oscillation and concentration effects of the optimal control policy. We show that hierarchies of semi-definite relaxations can also be constructed to deal numerically with noncon-vex optimal control problems with polynomial vector field and semialgebraic state constraints.