A fast well-conditioned interior point method for predictive control

Interior point methods (IPMs) have proven to be an efficient way of solving quadratic programming problems in predictive control. A linear system of equations needs to be solved in each iteration of an IPM. The ill-conditioning of this linear system in the later iterations of the IPM prevents the use of an iterative method in solving the linear system due to a very slow rate of convergence; in some cases the solution never reaches the desired accuracy. In this paper we propose the use of a well-conditioned, approximate linear system, which increases the rate of convergence of the iterative method. The computational advantage is obtained by the use of an inexact Newton method along with the use of novel preconditioners. Numerical results indicate that the computational complexity of our proposed method scales quadratically with the number of states and linearly with the horizon length.