Symmetric Hessian propagation for lifted collocation integrators in direct optimal control

Authors

• R. Quirynen, B. Houska, and M. Diehl.

Reference

• In Proceedings of the
  2016 American Control Conference,
  pages 1117-1123, Boston, USA, July 6-8, 2016. (accepted)

Abstract

Direct optimal control first discretizes the continuous time Optimal Control Problem (OCP) and then solves the resulting Nonlinear Program (NLP). Implicit integration schemes are used for the numerical simulation of stiff or implicitly defined dynamics. The propagation of sensitivities is often computationally demanding, especially when second order derivatives are needed for numerical optimization. This paper presents a tailored extension of the symmetric Hessian propagation technique to implicit integrators and proposes a novel exact Hessian based lifting approach, which combines advantages from direct collocation and multiple shooting. The algorithm takes Sequential Quadratic Programming (SQP) steps which are equivalent to those for direct collocation, while preserving many of the properties of a multiple shooting method such as its parallelizability. The proposed algorithm is implemented in the open-source ACADO code generation software. Its efficiency is illustrated on a benchmark case study from the field of time-optimal control.

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