Adaptive node placement for optimal control on system of multi-degree of freedom

Optimal control finds a control law for a system under optimality criterion. Numerical methods are necessary to solving an optimal control problem for sufficiently complex systems. Using quadrature methods base on fixed nodes, the Discrete Mechanics and Optimal Control (DMOC) method based on Newton quadrature by Marsden and the pseudospectral optimal control based on Gaussian quadrature are excellent for the numerical optimal control. The Adaptive Quadrature Optimal Control (AQUOC) by Ching uses an alternative method based on adaptive node placement, which the discretization node are concentrated in areas of high activity where precision is most needed during the optimization routine. Ching has verified the new algorithm via numerical solutions on systems of single degree of freedom. In this paper, through a rigorous formulation of the discretization using zero-order hold (ZOH) and 1^st order hold (FOH) interpolating input function respectively, the incorporation of AQUOC for linear time-invariant system of multi-degree of freedom is implemented and verified.