Robust Nonlinear Reduced-Order Model Predictive Control

TL;DR

This paper introduces a robust nonlinear reduced-order model predictive control approach that ensures stability and constraint satisfaction for high-dimensional systems by dynamically accounting for model reduction errors, demonstrated on a soft robot.

Contribution

A novel ROMPC scheme with error bounds that guarantees robustness, stability, and feasibility in controlling complex nonlinear systems.

Findings

Successfully applied to a high-dimensional soft robot with nearly 10,000 states

Ensures robust constraint satisfaction and asymptotic stability

Addresses model uncertainty due to dimensionality reduction

Abstract

Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality reduction introduces model uncertainty which can potentially compromise the stability and safety of the original high-dimensional system. In this work, we propose a novel reduced-order model predictive control (ROMPC) scheme to solve constrained optimal control problems for nonlinear, high-dimensional systems. To address the challenges of using ROMs in predictive control schemes, we derive an error bounding system that dynamically accounts for model reduction error. Using these bounds, we design a robust MPC scheme that ensures robust constraint satisfaction, recursive feasibility, and asymptotic stability. We demonstrate the effectiveness of our proposed method in simulations on a high-dimensional soft robot with nearly 10,000 states.