Preconditioners for inexact interior point methods for predictive control

Amir Shahzad, Eric C. Kerrigan, George A. Constantinides

Abstract: This paper presents a new method for solving a linear discrete-time finite horizon optimal control problem (FHOCP) with quadratic cost and linear constraints on the states and inputs. Such a FHOCP needs to be solved online, at each sampling instant, in predictive control. In order to solve such a FHOCP, it is necessary to solve a quadratic programming (QP) problem. The proposed technique uses an inexact interior-point method (IIPM) to solve the QP problem. This new technique is computationally more efficient than the Riccati Recursion method of Rao, Wright and Rawlings (Journal of Optimization Theory and Applications, 1998), when measured in terms of the number of floating point operations. The computational advantage is obtained by the use of an inexact Newton method, and with the use of novel preconditioners in the minimum residual (MINRES) method. The computational performance of this method is demonstrated by numerical results.