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A Controller Synthesis Framework for Weakly-Hard Control Systems

Marc Seidel, Martina Maggio, Frank Allgöwer

Abstract

Deadline misses are more common in real-world systems than one may expect. The weakly-hard task model has become a standard abstraction to describe and analyze how often these misses occur, and has been especially used in control applications. Most existing control approaches check whether a controller manages to stabilize the system it controls when its implementation occasionally misses deadlines. However, they usually do not incorporate deadline-overrun knowledge during the controller synthesis process. In this paper, we present a framework that explicitly integrates weakly-hard constraints into the control design. Our method supports various overrun handling strategies and guarantees stability and performance under weakly-hard constraints. We validate the synthesized controllers on a Furuta pendulum, a representative control benchmark. The results show that constraint-aware controllers significantly outperform traditional designs, demonstrating the benefits of proactive and informed synthesis for overrun-aware real-time control.

A Controller Synthesis Framework for Weakly-Hard Control Systems

Abstract

Deadline misses are more common in real-world systems than one may expect. The weakly-hard task model has become a standard abstraction to describe and analyze how often these misses occur, and has been especially used in control applications. Most existing control approaches check whether a controller manages to stabilize the system it controls when its implementation occasionally misses deadlines. However, they usually do not incorporate deadline-overrun knowledge during the controller synthesis process. In this paper, we present a framework that explicitly integrates weakly-hard constraints into the control design. Our method supports various overrun handling strategies and guarantees stability and performance under weakly-hard constraints. We validate the synthesized controllers on a Furuta pendulum, a representative control benchmark. The results show that constraint-aware controllers significantly outperform traditional designs, demonstrating the benefits of proactive and informed synthesis for overrun-aware real-time control.
Paper Structure (20 sections, 24 equations, 5 figures, 4 tables)

This paper contains 20 sections, 24 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background
  4. Modeling the Effects of Deadline Misses
  5. Modeling the Occurrence of Deadline Misses
  6. Control System Performance
  7. Controller Synthesis
  8. The framework
  9. System representation
  10. Weakly-hard graph
  11. Solve optimization problem
  12. Discussion
  13. Extensions to the framework
  14. Experimental Evaluation
  15. Experimental Setup
  16. ...and 5 more sections

Figures (5)

  • Figure 1: Workflow of the proposed controller design framework.
  • Figure 2: Example sequences, denoting M, H, R for a miss, hit, or recovery hit, respectively.
  • Figure 3: Switched system matrices for different actuator and overrun strategy combinations, omitting the time argument of $\alpha(\tilde{t})$ for conciseness of notation.
  • Figure 4: Example of a WH graph $\mathcal{G}$ for the $\texttt{AnyMiss}\,(3,5)$ constraint.
  • Figure 5: The Furuta pendulum used for experimental evaluation.

Theorems & Definitions (4)

  • Definition 1: WH constraint: AnyMiss
  • Definition 2: WH control system
  • Definition 3: $\ell_2$-performance for WH control systems
  • Definition 4: WH graph