Event-triggered Control and Online Learning for Networked Systems under Computational Delays

Xiaobing Dai; Armin Lederer; Zewen Yang; Sihua Zhang; Lu Wan; Yang Tang; Sandra Hirche

cs.LGAug 30, 2026

Event-triggered Control and Online Learning for Networked Systems under Computational Delays

Authors: Xiaobing Dai, Armin Lederer, Zewen Yang, Sihua Zhang, Lu Wan, Yang Tang, Sandra Hirche

Organizations: Chair of Information-oriented Control, School of Computation, Information and Technology, Technical University of Munich, Germany · Learning and Adaptive Systems Group, Department of Computer Science, ETH Zurich, Switzerland · Chair of Robotics and Systems Intelligence, Munich Institute of Robotics and Machine Intelligence, Technical University of Munich · Information Systems in the Built Environment, Eindhoven University of Technology, Eindhoven, Netherlands ·

Abstract

Online learning-based control is a promising approach to control uncertain systems, where unknown components are identified during operation to improve control performance. However, resource-intensive online learning algorithms introduce non-negligible computational delays, especially when executed on systems with limited local computational resources. To mitigate this, an in-network online learning-based control structure is employed by deploying the learning-based controller on a remote computation node and connecting it via a communication channel. In this paper, control performance guarantee is first established by deriving tracking error bound for the in-network control architecture, while accounting for computational delays. The derived tracking error bound allows for diverse communication and computation strategies under a specific condition, including time-/event-triggered mechanisms. Additionally, the trade-off between communication and computation performances is shown for a given desired control performance. Furthermore, to enhance the efficiency in both communication and computation, an efficient control framework with an asynchronous event-triggered mechanism in both control and online learning is devised under the existence of computational delay. The proposed event-triggered strategy is proven to achieve the same control performance as time-triggered scenario while excluding Zeno behavior. Finally, we derive an explicit expression of the proposed event-trigger condition for exponentially stabilizable systems, and demonstrate its effectiveness through simulations.

Figures & tables

Fig. 1 : Block diagram for in-network online learning-based control with event-triggered control and online data collection mechanism. The black blocks and lines imply fast computation and communication, while the computation and communication in red blocks and lines are slow.

Fig. 2 : Illustration of effects from computational delay.

Symbol	Description
$\Delta^{\rm{p}}(\cdot),\Delta^{\rm{u}}(\cdot)$	Computation time for prediction and update
$\bar{\Delta}^{\rm{p}},\bar{\Delta}^{\rm{u}}$	Upper bounds of $\Delta^{\rm{p}}(\cdot),\Delta^{\rm{u}}(\cdot)$
$\Delta(\cdot),\bar{\Delta}$	Total computation time and its upper bound
$\{t^{\rm{f}}_{p}\}_{p\in\mathbb{N}},\{t^{\rm{u}}_{k}\}_{k\in\mathbb{N}}$	Time sequence for online learning and control
$V(\cdot),\bar{V}(\cdot)$	Lyapunov function and its upper bound
$\phi_{p,1}\!(\cdot),\phi_{p,2}\!(\cdot,\cdot)$	Value of $\phi(\cdot,\cdot,\cdot)$ in $[t^{\rm{f}}_{p},\!t^{\rm{f}}_{p+1})$ and $[t^{\rm{f}}_{p+1},\!t^{\rm{f}}_{p+2})$

TABLE I : Summary of Main Notations in Section IV

Fig. 3 : a) Franka Emika Panda in its initial position. The red line represents the reference trajectory of the end effector, and the blue line is generated by online learning-based control with the proposed asynchronous event-triggered mechanism. b) The desired joint reference trajectory $\bm{q}_{r}=[q_{r,1},q_{r,2},q_{r,3},q_{r,4},q_{r,5},q_{r,6},q_{r,7}]^{T}$ over time $t$ , which is generalized by inverse kinematics.

Fig. 4 : The value of Lyapunov function $V(t)$ and tracking error $e(t)$ w.r.t time $t$ from $4$ learning-based control methods.

Fig. 5 : Prediction performance by using Double Trigger.

Panel of Figure 7 — Fig. 6 : Value of trigger function $\rho^{\rm{u}}(t)$ and $\rho^{\rm{f}}(t)$ over time $t$ and trigger instances for control update and online learning, respectively. It is obvious to see $\rho^{\rm{u}}(t)\leq 0$ for any $t\in\mathbb{R}_{0,+}$ , indicating $V(t)\leq\hat{V}(t)$ . This also means the control triggers occur at $t$ when $\rho^{\rm{u}}(t)=0$ , i.e., $V(t)=\hat{V}(t)$ . Due to the existence of computational delay, the value of $\rho^{\rm{f}}(\cdot)$ may greater than $0$ . However, the online learning triggered when $\rho^{\rm{f}}(\cdot)\geq 0$ ensures $\rho^{\rm{f}}(\cdot)<0$ after GP model update.

Event-Triggered Control

Event-triggered control updates controllers or communicates only when system conditions warrant, reducing resource use while maintaining stability and performance.

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Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland · Center for Artificial Intelligence, Helsinki, Finland

Agent Communication Protocols Feedback Control Model-Free RL Decentralized MARL Event-Triggered Control Multi-Agent Communication

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Event-triggered control provides a mechanism for avoiding excessive use of constrained communication bandwidth in networked multi-agent systems. However, most existing methods rely on accurate system models, which may be unavailable in practice. In this work, we propose a model-free, priority-driven reinforcement learning algorithm that learns communication priorities and control policies jointly from data in decentralized multi-agent systems. By learning communication priorities, we circumvent the hybrid action space typical in event-triggered control with binary communication decisions. We evaluate our algorithm on benchmark tasks and demonstrate that it outperforms the baseline method.

Abstract

Event-Triggered Control

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