Number Representation in Predictive Control

In predictive control a nonlinear optimization problem has to be solved at each sample instant. Solving this optimization problem in a computationally efficient and numerically reliable fashion on an embedded system is a challenging task. This paper presents results to reduce the computational requirements for solving fundamental problems that arise when implementing predictive controllers in finite precision arithmetic. By employing novel formulations and tailor-made optimization algorithms, this paper shows that computational resources can be reduced using very low precision arithmetic. We also present new mathematical results that enable computational savings to be made in the most numerically critical part of an optimization solver, namely the linear algebra kernel, using fixed-point arithmetic. Our theoretical results are supported by numerical results from implementations on a Field Programmable Gate Array (FPGA).