Auto-generated algorithms for nonlinear model predictive control on long and on short horizons

We present a code generation strategy for handling long prediction horizons in the context of real-time nonlinear model predictive control (NMPC). Existing implementations of fast NMPC algorithms use the real-time iteration (RTI) scheme and a condensing technique to reduce the number of optimization variables. Condensing results in a much smaller, but dense quadratic program (QP) to be solved at every time step. While this approach is well suited for short horizons, it leads to unnecessarily long execution times for problem formulations with long horizon. This paper presents a new implementation of auto-generated NMPC code based on a structure exploiting auto-generated QP solver. Utilizing such a QP solver, the condensing step can be avoided and execution times scale linearly with the horizon length instead of cubically. Our simulation results show that this approach significantly decreases the execution time of NMPC with long horizons. For a nonlinear test problem that comprises 9 states and 3 controls on a horizon with 50 time steps, an improvement by a factor of 2 was observed, reducing the execution time for one RTI to below 4 milliseconds on a 3 GHz CPU.