Numerical Algorithms of Quadratic Programming for Model Predictive Control
This dissertation thesis deals with the development of algorithms for the effective solution of quadratic programming problems for the embedded application of Model Predictive Control (MPC) MPC is a modern multivariable control method which involves solution of quadratic programming problem at each sample instant. The presented algorithms combine the active set strategy with the proportioning test to decide when to leave the actual active set. For the minimization in the face, we use the Newton directions implemented by the Cholesky factors updates. The performance of the algorithms is illustrated by numerical experiments and the results are compared with the state of the art solvers on benchmarks from MPC. The main contributions of this thesis are three new quadratic programming solvers together with their proof of convergence and properties analysis. Furthermore, the algorithm's implementation is described in detail showing how to exploit the structure of the face problem and resulting Newton direction to reduce the computational complexity of each iteration.