This technical note documents the equations for primal-dual interior-point quadratic programming
problem solver used for MPC. The algorithm exploits the special structure of the MPC problem
and is able to reduce the computational burden such that the computational burden scales with
prediction horizon length in a linear way rather than cubic, which would be the case if the structure
was not exploited. It is also shown how models used for design of model-based controllers, e.g.
linear quadratic and model predictive, can be linearized both at equilibrium and non-equilibrium
points, making the presented exstension of the controller formulation equivalent to that of the
extended Kalman filter compared to an ordinary Kalman filter.
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