  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.
