Direct optimal control for time-delay systems via a lifted multiple shooting algorithm

<p style='text-indent:20px;'>Aiming at efficient solution of optimal control problems for continuous nonlinear time-delay systems, a multiple shooting algorithm with lifted Runge-Kutta integrator is proposed. This in implicit form to remove the restriction smaller integration step sizes compared delays. A tangential predictor applied such that Newton iterations required can be reduced considerably. If one iteration applied, has same structure as direct collocation algorithms whereas derives condensed programming problem. Then, variational sensitivity equation decoupled from forward simulation by utilizing function theorem. Under certain conditions, this evaluation and derivative computation procedure proved convergent global order. Complexity analysis shows computational cost largely algorithm. parallelizable solver constructed embedding general-purpose solver. Simulations on numerical example demonstrate speed multi-threading implementation increased <inline-formula><tex-math id="M1">\begin{document}$ 36\% $\end{document}</tex-math></inline-formula> non-lifted one, factor id="M2">\begin{document}$ 6.64 traditional sequential algorithm; meanwhile, accuracy loss negligible.</p>