In model predictive control an optimization problem is solved in every time step, which in real-time applications has to be solved within a limited time frame. When applied on embedded hardware in fast changing systems it is important to use efficient solvers and crucial to guarantee that the optimization problem can be solved within the time frame.

In this thesis a path following controller which follows a motion plan given by a motion planner is implemented to steer a truck and trailer system. To solve the optimization problems which in this thesis are quadratic programs the three different solvers DAQP, qpOASES and OSQP are employed. The computational time of the active-set solvers DAQP, qpOASES and the operator splitting solver OSQP are compared, where the controller using DAQP was found the fastest and therefore most suited to use in this application of real-time model predictive control. 

A certification framework for the active-set method is used to give complexity guarantees on the controller using DAQP. The exact worst-case number of iterations when the truck and trailer system is following a straight path is presented. Furthermore, initial experiments show that given enough computational time/power the exact iteration complexity can be determined for every possible quadratic program that can appear in the controller.