[Paper Review] Decentralized event-triggered control over wireless sensor/actuator networks

Manuel Mazo, Paulo Tabuada|arXiv (Cornell University)|Apr 4, 2010

Network Time Synchronization Technologies4 references4 citations

TL;DR

This paper proposes a decentralized event-triggered control strategy for wireless sensor/actuator networks (WSANs) that enables centralized nonlinear controllers to be implemented without centralized coordination. By using local state measurements and adaptive triggering rules based on local error estimates, the method reduces communication and energy use while maintaining asymptotic stability, achieving near-centralized performance with minimal computational overhead on resource-constrained nodes.

ABSTRACT

In recent years we have witnessed a move of the major industrial automation providers into the wireless domain. While most of these companies already offer wireless products for measurement and monitoring purposes, the ultimate goal is to be able to close feedback loops over wireless networks interconnecting sensors, computation devices, and actuators. In this paper we present a decentralized event-triggered implementation, over sensor/actuator networks, of centralized nonlinear controllers. Event-triggered control has been recently proposed as an alternative to the more traditional periodic execution of control tasks. In a typical event-triggered implementation, the control signals are kept constant until the violation of a condition on the state of the plant triggers the re-computation of the control signals. The possibility of reducing the number of re-computations, and thus of transmissions, while guaranteeing desired levels of performance makes event-triggered control very appealing in the context of sensor/actuator networks. In these systems the communication network is a shared resource and event-triggered implementations of control laws offer a flexible way to reduce network utilization. Moreover reducing the number of times that a feedback control law is executed implies a reduction in transmissions and thus a reduction in energy expenditures of battery powered wireless sensor nodes.

Motivation & Objective

• Address the challenge of implementing centralized nonlinear controllers in decentralized wireless sensor/actuator networks (WSANs) where sensors are physically distributed and cannot access global state information.
• Overcome the limitations of observer-based or consensus-based approaches that require high communication and computational loads unsuitable for low-power sensor nodes.
• Develop a decentralized event-triggering mechanism that relies only on locally measured quantities, avoiding the need for full-state estimation or global observability.
• Ensure asymptotic stability of the closed-loop system while minimizing controller updates and communication events to reduce energy consumption in battery-powered nodes.
• Demonstrate that the proposed method achieves performance close to centralized event-triggered control, even without weak-coupling assumptions or centralized coordination.

Proposed method

• Adapt the centralized event-triggering framework from [18] to a decentralized setting by reformulating the triggering condition using only local state measurements at each sensor node.
• Introduce an adaptive triggering rule that dynamically adjusts the threshold for controller updates based on local error estimates, improving the inter-update time without compromising stability.
• Use a local error variable $ \varepsilon(t) $, defined as the difference between the actual state and the last transmitted state estimate, to determine when to recompute the control input.
• Apply a triggering condition of the form $ |\varepsilon(t)|^2 \leq \sigma |\xi(t) - x^*|^2 $, where $ \sigma $ is a tunable parameter derived from system parameters and stability margins.
• Implement the adaptation mechanism via Algorithm 1 with $ q = 1 $, allowing the threshold $ \theta(k) $ to evolve over time to extend inter-update intervals.
• Ensure stability by bounding the gradient of the Lyapunov function and using a compact set assumption to guarantee lower bounds on the gradient magnitude, enabling the derivation of a positive lower bound on the minimum inter-update time $ \tau_{\text{min}} = 0.1\,\text{ms} $.

Experimental results

Research questions

• RQ1 How can a centralized nonlinear controller be effectively decentralized for implementation over a wireless sensor/actuator network with limited communication and computation resources?
• RQ2 Can event-triggered control be adapted to decentralized WSANs without relying on global state information, observers, or consensus algorithms?
• RQ3 What is the minimal set of local information required to maintain stability and reduce communication frequency in decentralized event-triggered control?
• RQ4 How does the proposed adaptive triggering rule improve the inter-update time compared to non-adaptive decentralized implementations?
• RQ5 To what extent can decentralized event-triggered control approximate the performance of centralized event-triggered control in terms of update frequency and stability?

Key findings

• The decentralized event-triggered controller with adaptation achieves inter-update times very close to those of the centralized implementation, significantly outperforming non-adaptive decentralized versions.
• The minimum time between controller updates is bounded below by $ \tau_{\text{min}} = 0.1\,\text{ms} $, ensuring practical feasibility in real-time systems.
• The adaptive mechanism successfully extends the inter-update interval without degrading stability, as evidenced by the evolution of the adaptation vector $ \theta $ in Figure 3.
• Despite the lack of global state access, the decentralized implementation produces state trajectories nearly indistinguishable from the centralized case, confirming effective performance recovery.
• The method maintains asymptotic stability under the proposed triggering condition $ |\varepsilon(t)|^2 \leq \sigma |\xi(t) - x^*|^2 $ with $ \sigma = 0.0054^2 $, derived from system parameters and stability bounds.
• The computational and communication overhead remains low, making the approach suitable for deployment on low-power, resource-constrained sensor nodes in WSANs.