[Paper Review] Dynamic Event Generators for Event-Triggered Control Systems

Antoine Girard|arXiv (Cornell University)|Jan 10, 2013

Stability and Control of Uncertain Systems9 citations

TL;DR

This paper proposes dynamic event generators for event-triggered control systems by introducing an internal dynamic variable to improve performance. The method ensures closed-loop stability, guarantees a larger minimum inter-execution time than static generators, and reduces timing variability, leading to more predictable system behavior with significantly longer average inter-execution times.

ABSTRACT

Abstract. In this paper, we introduce a new class of event generators for event-triggered control systems. The main contribution lies in the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event generators. The stability of the resulting closed loop system is proved and the influence of design parameters on performances is discussed. It is also shown that the guaranteed lower bound on inter-execution times using a dynamic event generator cannot be smaller than that obtained for a classical static event generator. Some numerical results are provided to support these statements. They show that the inter-execution times are significantly larger in average and that their variability is smaller thus rendering the behavior of the closed loop system more predictable. 1.

Motivation & Objective

• To address the limitations of static event generators in event-triggered control systems, particularly in terms of inter-execution time predictability and performance.
• To design a new class of event generators that incorporate internal dynamics to improve system behavior and stability.
• To analyze the impact of design parameters on system performance and stability.
• To prove that dynamic event generators maintain or improve the lower bound on inter-execution times compared to static generators.
• To demonstrate through numerical results that dynamic event generators yield longer average inter-execution times and reduced variability.

Proposed method

• The proposed method introduces an internal dynamic variable within the event generator to adaptively determine when to trigger control updates.
• The dynamic variable evolves according to a differential equation, influencing the threshold for event triggering.
• Stability of the closed-loop system is proven using Lyapunov-based analysis, ensuring asymptotic stability under the proposed triggering mechanism.
• The design parameters of the dynamic variable are tuned to influence performance, including inter-execution time and system robustness.
• A comparison is made with classical static event generators to establish theoretical bounds on inter-execution times.
• Numerical simulations are conducted to validate the theoretical findings and illustrate performance improvements.

Experimental results

Research questions

• RQ1 How does the inclusion of an internal dynamic variable in event generators affect the stability of the closed-loop system?
• RQ2 What is the impact of design parameters on the performance and inter-execution time characteristics of dynamic event generators?
• RQ3 Can dynamic event generators guarantee a larger minimum inter-execution time than static event generators?
• RQ4 How does the variability of inter-execution times compare between dynamic and static event generators?
• RQ5 To what extent do dynamic event generators improve the predictability of control system behavior?

Key findings

• The closed-loop system using dynamic event generators is proven to be stable under the proposed triggering mechanism.
• The minimum inter-execution time guaranteed by dynamic event generators is not smaller than that of classical static event generators.
• Numerical results show that the average inter-execution time is significantly longer with dynamic event generators.
• The variability of inter-execution times is substantially reduced, leading to more predictable system behavior.
• The dynamic event generator improves performance by extending average inter-execution times while maintaining or improving stability guarantees.