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Robust Self-Triggered Control Approaches Optimizing Sensors Utilization with Asynchronous Measurements

Abbas Tariverdi

TL;DR

The paper tackles reducing sensor communication in networked control systems with asynchronous measurements by developing self-triggered state-feedback for linear plants. It introduces online and offline horizon-based sensor scheduling that maximizes inter-sample intervals while guaranteeing stability for perturbation-free systems and global uniform ultimate boundedness under bounded disturbances, respectively. Stability is certified via Lyapunov functions and LMIs, with online methods solving horizon optimization at runtime and offline methods using conic partitioning to enable lookup-based deployment. Simulations show substantial sensor utilization reductions (roughly 59–74%) compared to periodic sampling, highlighting the framework's potential for resource-efficient networked control under communication constraints.

Abstract

Most control systems run on digital hardware with limited communication resources. This work develops self-triggered control for linear systems where sensors update independently (asynchronous measurements). The controller computes an optimal horizon at each sampling instant, selecting which sensor to read over the next several time steps to maximize inter-sample intervals while maintaining stability. Two implementations address computational complexity. The online version solves an optimization problem at each update for theoretical optimality. The offline version precomputes optimal horizons using conic partitioning, reducing online computation to a lookup. Both guarantee exponential stability for unperturbed systems and global uniform ultimate boundedness for systems with bounded disturbances. Simulations demonstrate 59-74\% reductions in sensor utilization compared to periodic sampling. The framework enables resource-efficient control in networked systems with communication constraints.

Robust Self-Triggered Control Approaches Optimizing Sensors Utilization with Asynchronous Measurements

TL;DR

The paper tackles reducing sensor communication in networked control systems with asynchronous measurements by developing self-triggered state-feedback for linear plants. It introduces online and offline horizon-based sensor scheduling that maximizes inter-sample intervals while guaranteeing stability for perturbation-free systems and global uniform ultimate boundedness under bounded disturbances, respectively. Stability is certified via Lyapunov functions and LMIs, with online methods solving horizon optimization at runtime and offline methods using conic partitioning to enable lookup-based deployment. Simulations show substantial sensor utilization reductions (roughly 59–74%) compared to periodic sampling, highlighting the framework's potential for resource-efficient networked control under communication constraints.

Abstract

Most control systems run on digital hardware with limited communication resources. This work develops self-triggered control for linear systems where sensors update independently (asynchronous measurements). The controller computes an optimal horizon at each sampling instant, selecting which sensor to read over the next several time steps to maximize inter-sample intervals while maintaining stability. Two implementations address computational complexity. The online version solves an optimization problem at each update for theoretical optimality. The offline version precomputes optimal horizons using conic partitioning, reducing online computation to a lookup. Both guarantee exponential stability for unperturbed systems and global uniform ultimate boundedness for systems with bounded disturbances. Simulations demonstrate 59-74\% reductions in sensor utilization compared to periodic sampling. The framework enables resource-efficient control in networked systems with communication constraints.

Paper Structure

This paper contains 31 sections, 4 theorems, 73 equations, 17 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. System Description and Problem Statement
  3. System Description
  4. System Reformulation
  5. Motivational Example
  6. Problem Statement
  7. Main Results: Perturbation-free Case
  8. Proposed Self Triggering Mechanism and Stability Analysis: Online case
  9. Self Triggering Mechanism and Stability Analysis
  10. Implementation Algorithm
  11. Proposed Self Triggering Mechanism and Stability Analysis: Offline case
  12. Self Triggering Mechanism and Stability Analysis
  13. Implementation Algorithm
  14. Main Results: Perturbed Case
  15. System Reformulation
  16. ...and 16 more sections

Key Result

Proposition 1

Consider a scalar $\beta>0$, a constant sampling interval $T$, and a matrix $P=P^T\succ0$ such that Then, system Hdsyst with the self-triggering mechanism defined by with is exponentially stable with the decay rate of $\beta/2$, where $\zeta_k = x^T_k (\Phi^T_{\sigma} P \Phi_{\sigma} -e^{(-\beta |\sigma |T) }P )x_k$.

Figures (17)

  • Figure 1: System description with asynchronous measurement.
  • Figure 2: System state discretization using asynchronous measurement.
  • Figure 3: Evolution of the average of sampling intervals for each sensor with respect to modulus of the maximum eigenvalue and stabilizing sampling intervals
  • Figure 4: Covering the state space of dimension 2 with $N$ conic regions $\mathcal{R}_c, c \in \{1,\cdots,N\}$
  • Figure 5: The illustration of three regions $\mathcal{E}(P,1)$, $\mathcal{E}(P,\mu)$, and $\mathcal{B}(0,\psi)$.
  • ...and 12 more figures

Theorems & Definitions (14)

  • Proposition 1
  • proof
  • Remark 1
  • Proposition 2
  • proof
  • Remark 2
  • Definition 1
  • Proposition 3
  • proof
  • Remark 3
  • ...and 4 more