Multi-objective Co-design for model predictive control with an FPGA

Bulat Khusainov, Eric C. Kerrigan, George A. Constantinides

Abstract: In order to achieve the best possible performance of a model predictive controller (MPC) for a given set of resources, the software algorithm and computational platform have to be designed simultaneously. Moreover, in practical applications the controller design problem has a multi-objective nature: performance is traded off against computational hardware resource usage, namely time, energy and space. This paper proposes formulating an MPC design problem as a multi-objective optimization (MOO) problem in order to explore the design trade-offs in a systematic way. Since the design objectives in the resulting MOO problem are expensive to evaluate, i.e. evaluation requires time consuming simulations, most of the classical and evolutionary MOO algorithms cannot be employed for this class of design problems. For this reason a practical MOO algorithm that can deal with expensive-to-evaluate functions is presented. The algorithm is based on Kriging and the hypervolume criterion that was recently proposed in the expensive optimization literature. A numerical example for a fast gradient-based controller design shows that the proposed approach can efficiently explore optimal performance-resource trade-offs.