Adaptive node placement for Optimal Control

Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. Most optimal control problems are sufficiently complex such that numerical methods are necessary to compute a solution. Some of the more prominent works on the numerical optimal control are the discrete mechanics and optimal control (DMOC) method based on Newton quadrature by Marsden and the pseudospectral optimal control based on Gaussian quadrature. As both quadrature methods are based on fixed nodes, this paper proposes an alternative method based on adaptive node placement. The node locations are allowed to vary during the optimization routine such that they can be concentrated in areas of high activity where precision is most needed. The new algorithm is verified via numerical solutions.