Efficient NMPC for nonlinear models with linear subsystems

Real-time optimal control algorithms for fast, mechatronic systems need to be run on embedded hardware and they need to respect tight timing constraints. When using nonlinear models, the simulation and generation of sensitivities forms a computationally demanding part of any algorithm. Automatic code generation of Implicit Runge-Kutta (IRK) methods has been shown to reduce its CPU time significantly. However, a typical model also shows a lot of structure that can be exploited in a rather elegant and efficient way. The focus of this paper is on nonlinear models with linear subsystems. With the proposed model formulation, the new auto generated integrators can be considered a powerful generalization of other solvers, e.g. those that support quadrature variables. A speedup of up to 5 - 10 is shown in the integration time for two examples from the literature.