Semi-definite relaxations for optimal control problems with oscillation and concentration effects

0470207 - ÚTIA 2018 RIV FR eng J - Journal Article
Claeys, M. - Henrion, D. - Kružík, Martin
Semi-definite relaxations for optimal control problems with oscillation and concentration effects.
ESAIM-Control Optimisation and Calculus of Variations. Roč. 23, č. 1 (2017), s. 95-117. ISSN 1292-8119. E-ISSN 1262-3377
Institutional support: RVO:67985556
Keywords : optimal control * impulsive control * semidefinite programming
OECD category: Pure mathematics
Impact factor: 1.225, year: 2017
http://library.utia.cas.cz/separaty/2017/MTR/kruzik-0470207.pdf

Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed
for state-constrained optimal control problems featuring oscillation phenomena, by relaxing controls as Young measures. These semi-definite relaxations were later on extended to optimal control problems depending linearly on the control 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 introduced originally by DiPerna and Majda in the partial differential equations literature 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 nonconvex optimal control problems with polynomial vector field and semialgebraic state constraints
Permanent Link: http://hdl.handle.net/11104/0270856