Fast auto generated ACADO integrators and application to MHE with multi-rate measurements

Algorithms for real-time, embedded optimization need to run within tight computational times, and preferably on embedded control hardware for which only limited computational power and memory is available. A computationally demanding step of these algorithms is the model simulation with sensitivity generation. This paper presents an implementation of code generation for Implicit Runge-Kutta (IRK) methods with efficient sensitivity generation, which outperforms other solvers for the targeted applications. The focus of this paper will be on the extension of the proposed tool to the integration of index-1 Differential Algebraic Equations (DAE), and continuous output functions, which are crucial for e.g. performing sensor fusion with measurements provided at very high sampling rates. The new tool is provided with a powerful MATLAB interface. It is illustrated in simulation for the trajectory estimation of a mechanical system modeled by complex Differential-Algebraic equations, using sensor information provided at fast, multi-rate sampling frequencies.