Towards a fixed point QP solver for predictive control

There is a need for high speed, low cost and low energy solutions for convex quadratic programming to enable model predictive control (MPC) to be implemented in a wider set of applications than is currently possible. For most quadratic programming (QP) solvers the computational bottleneck is the solution of systems of linear equations, which we propose to solve using a fixed-point implementation of an iterative linear solver to allow for fast and efficient computation in parallel hardware. However, fixed point arithmetic presents additional challenges, such as having to bound peak values of variables and constrain their dynamic ranges. For these types of algorithms the problems cannot be automated by current tools. We employ a preconditioner in a novel manner to allow us to establish tight analytical bounds on all the variables of the Lanczos process, the heart of modern iterative linear solving algorithms. The proposed approach is evaluated through the implementation of a mixed precision interior-point controller for a Boeing 747 aircraft. The numerical results show that there does not have to be a loss of control quality by moving from floating-point to fixed-point.