Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quantum optimization for Nonlinear Model Predictive Control

Carlo Novara, Mattia Boggio, Deborah Volpe

TL;DR

A quantum computing approach is proposed for the solution of the NMPC optimization problem, which has the potential to considerably decrease the computational time and/or enhance the solution quality compared to classical algorithms.

Abstract

Nonlinear Model Predictive Control (NMPC) is a general and flexible control approach, used in many industrial contexts, and is based on the online solution of a nonlinear optimization problem. This operation requires in general a high computational cost, which may compromise the NMPC implementation in ``fast'' applications, especially if a large number variables is involved. To overcome this issue, we propose a quantum computing approach for the solution of the NMPC optimization problem. Assuming the availability of an efficient quantum computer, the approach has the potential to considerably decrease the computational time and/or enhance the solution quality compared to classical algorithms.

Quantum optimization for Nonlinear Model Predictive Control

TL;DR

A quantum computing approach is proposed for the solution of the NMPC optimization problem, which has the potential to considerably decrease the computational time and/or enhance the solution quality compared to classical algorithms.

Abstract

Nonlinear Model Predictive Control (NMPC) is a general and flexible control approach, used in many industrial contexts, and is based on the online solution of a nonlinear optimization problem. This operation requires in general a high computational cost, which may compromise the NMPC implementation in ``fast'' applications, especially if a large number variables is involved. To overcome this issue, we propose a quantum computing approach for the solution of the NMPC optimization problem. Assuming the availability of an efficient quantum computer, the approach has the potential to considerably decrease the computational time and/or enhance the solution quality compared to classical algorithms.

Paper Structure

This paper contains 17 sections, 1 theorem, 44 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notation
  3. Nonlinear MPC
  4. Plant to control
  5. NMPC formulation
  6. Input sequence dimension reduction
  7. Receding horizon strategy
  8. Polynomial MPC
  9. Polynomial prediction algorithm
  10. Polynomial MPC
  11. Quantum MPC with input-affine model and saturation constraints
  12. Binary encoding technique
  13. Quantum MPC with input-affine model and saturation constraints
  14. Quantum MPC with input-polynomial model and polynomial constraints
  15. Quantum MPC with input-polynomial model and saturation constraints
  16. ...and 2 more sections

Key Result

Theorem 1

Let Assumptions A1-A3 hold true. Let $\xi^{*}$ be a global solution of (eq:opt-3a), $\Xi^{*}=RS(\xi^{*},n_{b},n_{c})^{\top}$ and $\breve{c}^{*}=\underline{c}+C_{b}\Xi^{*}\eta$. Let $c^{*}$ be the global solution of (eq:opt-2) closest to $\breve{c}^{*}$. Then, for a sufficiently large $n_{b}$, Moreover, a finite positive constant $\gamma_{P}$ (independent of $n_{b}$) exists such that

Theorems & Definitions (5)

  • Remark 1
  • Remark 2
  • Remark 3
  • Theorem 1
  • Remark 4