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Event-triggered Robust Model Predictive Control under Hard Computation Resource Constraints

Alexander Gräfe, Sebastian Trimpe

TL;DR

This paper tackles controlling $M_s$ independent nonlinear systems using MPC when a central server can only recompute trajectories for at most $M_c<M_s$ systems per time step. It introduces an event-triggered robust MPC (ET-MPC) that prioritizes which systems are recomputed, ensuring constraint satisfaction and gISS stability for all systems while limiting peak computational load. A priority-based trigger bounds the prediction error between actual and predicted states via a function $\tilde V_{\max}(\hat w)$, enabling a robust MPC with constraint tightening and a final-state policy. Theoretical results establish recursive feasibility and gISS under bounded disturbances, and experiments with quadcopters demonstrate the ability to stabilize multiple agents with reduced central computation, highlighting practical scalability and resource efficiency.

Abstract

Model predictive control (MPC) is capable of controlling nonlinear systems with guaranteed constraint satisfaction and stability. However, MPC requires solving optimization problems online periodically, which often exceeds the local system's computational capabilities. A potential solution is to leverage external processing, such as a central industrial server. Yet, this central computer typically serves multiple systems simultaneously, leading to significant hardware demands due to the need to solve numerous optimization problems concurrently. In this work, we tackle this challenge by developing an event-triggered model predictive control (ET-MPC) that provably stabilizes multiple nonlinear systems under disturbances while solving only optimization problems for a fixed-size subset at any given time. Unlike existing ET-MPC methods, which primarily reduce average computational load yet still require hardware capable of handling all systems simultaneously, our approach reduces the worst-case computational load. This significantly lowers central server hardware requirements by diminishing peak computational demands. We achieve our improvements by leveraging recent advancements in distributed event-triggered linear control and integrating them with a robust MPC that employs constraint tightening.

Event-triggered Robust Model Predictive Control under Hard Computation Resource Constraints

TL;DR

This paper tackles controlling independent nonlinear systems using MPC when a central server can only recompute trajectories for at most systems per time step. It introduces an event-triggered robust MPC (ET-MPC) that prioritizes which systems are recomputed, ensuring constraint satisfaction and gISS stability for all systems while limiting peak computational load. A priority-based trigger bounds the prediction error between actual and predicted states via a function , enabling a robust MPC with constraint tightening and a final-state policy. Theoretical results establish recursive feasibility and gISS under bounded disturbances, and experiments with quadcopters demonstrate the ability to stabilize multiple agents with reduced central computation, highlighting practical scalability and resource efficiency.

Abstract

Model predictive control (MPC) is capable of controlling nonlinear systems with guaranteed constraint satisfaction and stability. However, MPC requires solving optimization problems online periodically, which often exceeds the local system's computational capabilities. A potential solution is to leverage external processing, such as a central industrial server. Yet, this central computer typically serves multiple systems simultaneously, leading to significant hardware demands due to the need to solve numerous optimization problems concurrently. In this work, we tackle this challenge by developing an event-triggered model predictive control (ET-MPC) that provably stabilizes multiple nonlinear systems under disturbances while solving only optimization problems for a fixed-size subset at any given time. Unlike existing ET-MPC methods, which primarily reduce average computational load yet still require hardware capable of handling all systems simultaneously, our approach reduces the worst-case computational load. This significantly lowers central server hardware requirements by diminishing peak computational demands. We achieve our improvements by leveraging recent advancements in distributed event-triggered linear control and integrating them with a robust MPC that employs constraint tightening.
Paper Structure (7 sections, 6 theorems, 45 equations, 3 figures)

This paper contains 7 sections, 6 theorems, 45 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM SETTING
  3. EVENT-TRIGGER FOR RESOURCE CONSTRAINED ROBUST MPC
  4. ROBUST MODEL PREDICTIVE CONTROL
  5. EXPERIMENTS
  6. CONCLUSION
  7. ACKNOWLEDGMENTS

Key Result

Lemma 1

If Assumption as:lipschitz holds, then $\forall\hat{w} \in \mathbb{R}^+_0$, $\forall t\in\mathbb{N}_0$ with $p = \lceil\frac{M_\mathrm{s}}{M_\mathrm{c}}\rceil$

Figures (3)

  • Figure 1: Overview of the system setup. A central computer controls $M_\mathrm{s}$ independent systems using MPC. Due to its limited resources, it can only handle $M_\mathrm{c} < M_\mathrm{s}$ MPC optimizations per time step. To address this limitation, an event-triggered approach is employed to prioritize and select the systems in most need (green box).
  • Figure 2: Example trajectory flown by three quadcopters, while the central computer controls only one of them at a time.
  • Figure 3: Behavior of ten controlled quadcopters for different amplitudes of disturbances and computation resources. The plot shows the mean absolute deviation of the position from 0. Areas marked as red (value 1) are unstable.

Theorems & Definitions (16)

  • Definition 1: gISS
  • Remark 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Remark 2
  • Remark 3
  • ...and 6 more