New publication: “Perturbed-analytic direct transcription for optimal control (PADOC)”

The Aircraft Operations Lab UC3M has a new paper on trajectory optimisation. On this occasion, the research article has been written by PhD student Amin Jafarimoghaddam and professor Manuel Soler, and published by the Wiley online library.


The herein coined PADOC (perturbed-analytic direct transcription for optimal control) stands for a new transcription method for direct trajectory optimization. We construct PADOC on a novel segmented decomposition method that provides series solutions for nonlinear problems. To transcribe the infinite dimensional problem into a finite one, PADOC comes along with a new solution approach, namely, the herein coined average nonlinear programming (aNLP). The aNLP theorem suggests generating a staircase optimal solution (low resolution) and turning it into a distributed optimal solution (high resolution) by exploiting the Hamiltonian of the problem. The analytic architecture provides PADOC with an analytic connection of a truncated order between the discrete nodes of the solution. This renders stability, accuracy within an analytic resolution, robustness, and a cut-down in the number of the decision variables in the frame of NLP. We also prove that the multipliers associated with the Karush–Kuhn–Tucker optimality conditions in the frame of NLP (as transcribed by PADOC) correspond to a backward analytic solution for the costate equations. We finally show distinct features of PADOC through some examples.

Perturbed-analytic direct transcription for optimal control (PADOC). Amin Jafarimoghaddam, Manuel Soler. Optimal Control Applications and Methods. 2023. Doi:

Leave a Reply

%d bloggers like this: