Model Predictive Control for Finite Input Systems using the D-Wave Quantum Annealer

Daisuke Inoue,Hiroaki Yoshida

doi:10.1038/s41598-020-58081-9

Abstract

The D-Wave quantum annealer has emerged as a novel computational architecture that is attracting significant interest, but there have been only a few practical algorithms exploiting the power of quantum annealers. Here we present a model predictive control (MPC) algorithm using a quantum annealer for a system allowing a finite number of input values. Such an MPC problem is classified as a non-deterministic polynomial-time-hard combinatorial problem, and thus real-time sequential optimization is difficult to obtain with conventional computational systems. We circumvent this difficulty by converting the original MPC problem into a quadratic unconstrained binary optimization problem, which is then solved by the D-Wave quantum annealer. Two practical applications, namely stabilization of a spring-mass-damper system and dynamic audio quantization, are demonstrated. For both, the D-Wave method exhibits better performance than the classical simulated annealing method. Our results suggest new applications of quantum annealers in the direction of dynamic control problems.

Highlights

Since quantum annealer 2000Q was released from D-Wave Systems Inc., research on quantum computing has rapidly progressed[1,2,3,4]
Finding the optimal input for such systems becomes drastically difficult as the size of the problem increases, because this problem is classified as a non-deterministic polynomial-time (NP)-hard combinatorial optimization problem
We first give a method to transform the original model predictive control (MPC) problem into a quadratic unconstrained binary optimization (QUBO) problem, which is the only class of problem that the Toyota Central R&D Labs., Inc., Bunkyo-ku, Tokyo, 112-0004, Japan. *email: daisuke-inoue@mosk.tytlabs.co.jp www.nature.com/scientificreports/

Summary

Introduction

Since quantum annealer 2000Q was released from D-Wave Systems Inc., research on quantum computing has rapidly progressed[1,2,3,4]. The problem of finding input sequence u(t) := [u(t) ⋯ u(t + N − 1)]⊤ that minimizes the evaluation function 3, while observing states x(t) at time t, u*(t) := argminu(t)∈ NH, (4) The average value in each method is 4.22 × 108 and 5.62 × 108, respectively, and the value in the quantum annealing is suppressed to 0.75 times that in the simulated annealing.

Results

Conclusion