2023/10/31 by Jonathan Frey, Frey, Jonathan, Katrin Baumgärtner +3 · 1 citation
Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2310.20390
openalex publication_date 2023/10/31 · openalex created_date 2023/11/02 · openalex updated_date 2026/08/01
This work proposes an efficient treatment of continuous-time optimal control problem (OCP) with long horizons and nonlinear least-squares costs. The Gauss-Newton Runge-Kutta (GNRK) integrator is presented which provides a high-order cost integration. Crucially, the Hessian of the cost terms required within an SQP-type algorithm is approximated with a Gauss-Newton Hessian. Moreover, L2 penalty formulations for constraints are shown to be particularly effective for optimization with GNRK. An efficient implementation of GNRK is provided in the open-source software framework acados. We demonstrate the effectiveness of the proposed approach and its implementation on an illustrative example showing a reduction of relative suboptimality by a factor greater than 10 while increasing the runtime by only 10 %.