A two-timescale discretization scheme for collocation

The development of a two-timescale discretization scheme for collocation is presented. This scheme allows a larger discretization to be utilized for smoothly varying state variables and a second finer discretization to be utilized for state variables having higher frequency dynamics. As such, the discretization scheme can be tailored to the dynamics of the particular state variables. In so doing, the size of the overall Nonlinear Programming (NLP) problem can be reduced significantly. Two two-timescale discretization architecture schemes are described. Comparison of results between the two-timescale method and conventional collocation show very good agreement. Differences of less than 0.5 percent are observed. Consequently, a significant reduction (by two-thirds) in the number of NLP parameters and iterations required for convergence can be achieved without sacrificing solution accuracy.