Two-timescale discretization scheme for collocation

The development of a two-timescale discretization scheme for collocation is presented. This scheme allows a coarser discretization to be used for slowly varying state variables and a second finer discretization to be used for state variables having higher-frequency dynamics. That is, the discretization scheme can be tailored to the dynamics of the particular state variables. Consequently, the size of the overall nonlinear programming problem can be reduced significantly. Two two-timescale discretization architecture schemes are described. Comparison of results between the two-timescale method and conventional single-timescale collocation shows very good agreement. When the two-timescale discretization is used in combination with the sparse nonlinear optimizer SNOPT, a significant reduction (by more than 60%) in the number of nonlinear programming parameters required for the transcription of the problem and iterations necessary for convergence can be achieved without sacrificing solution accuracy.