[Paper Review] Asynchronous Computation of Tube-based Model Predictive Control

Jérôme Sieber, Andrea Zanelli+3 more|arXiv (Cornell University)|Nov 24, 2022

Advanced Control Systems Optimization1 citations

TL;DR

This paper proposes an asynchronous computation mechanism for system-level tube model predictive control (SLTMPC) that decouples nominal trajectory optimization from tube computation, enabling high-frequency control updates while maintaining recursive feasibility. By running the nominal trajectory computation (primary process) at high frequency and updating tubes (secondary process) asynchronously, the method reduces computational burden and improves performance over traditional tube-MPC, with numerical results showing a 28% reduction in closed-loop cost compared to standard tube-MPC.

ABSTRACT

Tube-based model predictive control (MPC) methods bound deviations from a nominal trajectory due to uncertainties in order to ensure constraint satisfaction. While techniques that compute the tubes online reduce conservativeness and increase performance, they suffer from high and potentially prohibitive computational complexity. This paper presents an asynchronous computation mechanism for system level tube-MPC (SLTMPC), a recently proposed tube-based MPC method which optimizes over both the nominal trajectory and the tubes. Computations are split into a primary and a secondary process, computing the nominal trajectory and the tubes, respectively. This enables running the primary process at a high frequency and moving the computationally complex tube computations to the secondary process. We show that the secondary process can continuously update the tubes, while retaining recursive feasibility of the primary process.

Motivation & Objective

• To address the high computational complexity of online tube optimization in SLTMPC for constrained linear systems with additive disturbances.
• To enable real-time implementation of SLTMPC by decoupling computationally intensive tube computations from the primary control loop.
• To maintain recursive feasibility and constraint satisfaction while asynchronously updating tube sequences.
• To demonstrate improved performance and reduced conservativeness compared to conventional tube-based MPC.

Proposed method

• The method splits SLTMPC into a primary process (nominal trajectory optimization) and a secondary process (tube computation), enabling asynchronous execution.
• The primary process uses a memory of past and updated tube sequences, fusing them via convex combinations to maintain recursive feasibility.
• A new scaled terminal set is introduced to support recursive feasibility under asynchronous tube updates.
• The secondary process continuously optimizes tube sequences using an H∞-cost or nominal cost, with results passed to the primary process at intervals.
• The fusion mechanism combines old and new tubes using convex weights, ensuring stability and feasibility even when tubes are updated asynchronously.
• The approach is generalizable to other online tube-MPC formulations, such as configuration-constrained tubes.

Experimental results

Research questions

• RQ1 Can SLTMPC be implemented at higher control frequencies by decoupling tube computation from nominal trajectory optimization?
• RQ2 How can recursive feasibility be preserved when tubes are asynchronously updated in the primary control loop?
• RQ3 What performance gains are achievable by dynamically updating tubes online compared to fixed offline tubes?
• RQ4 How does the asynchronous mechanism compare in computational cost and closed-loop performance to standard tube-MPC and full online SLTMPC?
• RQ5 What is the impact of tube fusion strategies on constraint satisfaction and robustness?

Key findings

• The asynchronous SLTMPC method achieves a mean closed-loop cost of 67.36, representing a 28% reduction compared to tube-MPC (85.92) and a 12% improvement over full online SLTMPC (59.07).
• The minimum solve time for the primary process (1.74 ms) is comparable to tube-MPC (1.52 ms), enabling high-frequency control despite online tube optimization.
• The primary process maintains recursive feasibility by fusing multiple tube sequences using convex combinations, even when tubes are updated asynchronously.
• The region of attraction (RoA) of the asynchronous SLTMPC is significantly larger than that of standard tube-MPC, demonstrating reduced conservativeness due to online tube adaptation.
• At t = 20, tube updates cease as the trajectory approaches the origin, indicating that the system intelligently avoids unnecessary tube re-optimization.
• The method successfully replaces old tube sequences with new ones (e.g., λ2 = 0 at t = 5), with dashed lines in figures indicating effective tube replacement and reduced reliance on outdated tubes.