Abstract:

Optimization based control is widely used for stabilizing control of constrained linear dynamical systems. We present an Infeasible Interior Point Method (IIPM) for the solution of convex quadratic programs, such as those arising in Model Predictive Control (MPC) of constrained linear dynamical systems, using a novel homogeneous formulation [1]. The homogenization is applied on a slacked reformulation of the QP. We describe a tailored step computation in the IIPM that addresses the potential loss of sparsity resulting from the homogenization. We present arguments for the effectiveness of the slacked formulation in warm-start of IIPM. The algorithm is implemented in Julia. Numerical experiments on the formulation are provided comparing the proposed approach against existing IPM implementations on feasible and infeasible quadratic programs. We also demonstrate that the warms-starts of the proposed IIPM reduces the computational time by 50% on an MPC application.