Preconditioned Krylov iterations and condensing in interior point MPC method

We investigate using Krylov subspace iterative methods in model predictive control (MPC), where the prediction model is given by linear or linearized systems with linear inequality constraints on the state and the input, and the performance index is quadratic. The inequality constraints are treated by the primal-dual interior point method. We indicate condition numbers of several linear systems, which determine the search direction in the Newton method, and propose a new preconditioner for one of the systems. Numerical results illustrate convergence of Krylov methods with and without preconditioning and demonstrate that our preconditioning reduces the number of Krylov iterations 2-10 times.