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A Robust Model Predictive Control Method for Networked Control Systems

Severin Beger, Sandra Hirche

TL;DR

The paper tackles robust control over networks with delays and packet drops by introducing a prediction-consistent MPC framework coupled with tube MPC, designed for UDP-like, non-synchronous networks. It formalizes a precise mechanism for maintaining consistent predictions across plant and remote controller via time-stamped packets and buffered trajectories, ensuring stability and feasibility. Theoretical results establish prediction-consistency under mild assumptions and provide a bound on the disturbance-invariant tube, while simulations on a Cart Pole and a CSTR demonstrate improved constraint satisfaction and robustness over nominal MPC. The proposed approach is practical for resource-limited remote computation and general-purpose networks, with room for online adaptation and learning-enabled extensions.

Abstract

Robustly compensating network constraints such as delays and packet dropouts in networked control systems is crucial for remotely controlling dynamical systems. This work proposes a novel prediction consistent method to cope with delays and packet losses as encountered in UDP-type communication systems. The augmented control system preserves all properties of the original model predictive control method under the network constraints. Furthermore, we propose to use linear tube MPC with the novel method and show that the system converges robustly to the origin under mild conditions. We illustrate this with simulation examples of a cart pole and a continuous stirred tank reactor.

A Robust Model Predictive Control Method for Networked Control Systems

TL;DR

The paper tackles robust control over networks with delays and packet drops by introducing a prediction-consistent MPC framework coupled with tube MPC, designed for UDP-like, non-synchronous networks. It formalizes a precise mechanism for maintaining consistent predictions across plant and remote controller via time-stamped packets and buffered trajectories, ensuring stability and feasibility. Theoretical results establish prediction-consistency under mild assumptions and provide a bound on the disturbance-invariant tube, while simulations on a Cart Pole and a CSTR demonstrate improved constraint satisfaction and robustness over nominal MPC. The proposed approach is practical for resource-limited remote computation and general-purpose networks, with room for online adaptation and learning-enabled extensions.

Abstract

Robustly compensating network constraints such as delays and packet dropouts in networked control systems is crucial for remotely controlling dynamical systems. This work proposes a novel prediction consistent method to cope with delays and packet losses as encountered in UDP-type communication systems. The augmented control system preserves all properties of the original model predictive control method under the network constraints. Furthermore, we propose to use linear tube MPC with the novel method and show that the system converges robustly to the origin under mild conditions. We illustrate this with simulation examples of a cart pole and a continuous stirred tank reactor.

Paper Structure

This paper contains 10 sections, 2 theorems, 18 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. A simple consistent prediction method
  4. Properties of the method
  5. Simulation Examples
  6. Cart Pole
  7. Continuous Stirred Tank Reactor
  8. Discussion
  9. Conclusion
  10. Proof of Lemma \ref{['thm:Lemma1']}

Key Result

Lemma IV.1

If assumptions (A1-A4) hold, the proposed method for delay and packet loss compensation using model predictive control methodologies in networked control systems under the influence of delays and packet dropouts is prediction consistent in the sense of Definition def:PredictionConsistency.

Figures (9)

  • Figure 1: Considered setup. The local controller forwards measurements to the remote side and receives actuation signals from the remote controller over a lossy network.
  • Figure 2: Plant side algorithm. Top part handles incoming control packets, middle part checks on prediction consisteny, bottom task computes and executes the control input.
  • Figure 3: Remote controller algorithm. Top part describes checks for measurement and prediction consistency, the middle part determines the state prediction, the bottom part solves the OCP.
  • Figure 4: Worst case delay and dropout scenario of the presented method. Arrows represent packets. $\bar{\tau}_{RTT} = \bar{n}_{l} = 2$.
  • Figure 5: Position and tilt angle of the balance robot. We compare a nominal MPC with the tube based MPC method.
  • ...and 4 more figures

Theorems & Definitions (6)

  • Definition 1
  • Lemma IV.1
  • proof
  • Theorem IV.2
  • proof
  • proof