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# Numerical Algorithms of Quadratic Programming for Model Predictive Control[edit]

**Author**: Ondřej Šantin

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.

**Ondřej Šantin**, mailto:Ondrej.Santin@Honeywell.com