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Robust Self-Triggered Control Approaches Optimizing Sampling Sequences with Synchronous Measurements

Abbas Tariverdi

TL;DR

The paper tackles resource-efficient control for linear systems by developing self-triggered sampling schemes that precompute the next sampling horizon to maximize inter-sampling intervals while preserving stability. It presents both online and offline variants for perturbation-free and perturbed (bounded disturbance) cases, establishing exponential stability via Lyapunov LMIs and global uniform ultimate boundedness (GUUB) with disturbance handling. Key contributions include horizon-based optimization over finite horizons, conic-region offline partitioning, and corresponding algorithms (Schur-LMI conditions and S-procedure-based LMIs) that guarantee stability or GUUB. The work demonstrates, through simulations, that substantial reductions in sampling frequency are achievable without compromising performance, making the approach suitable for embedded and networked control systems under tight computational and communication constraints.

Abstract

Feedback control algorithms traditionally rely on periodic execution on digital platforms. While this simplifies design and analysis, it often leads to inefficient resource usage (e.g., CPU, network bandwidth) in embedded control and shared networks. This work investigates self-triggering implementations of linear controllers in sampled-data systems with synchronous measurements. Our approach precomputes the next sampling sequence over a finite horizon based on current state information. We introduce a novel optimal self-triggering scheme that guarantees exponential stability for unperturbed systems and global uniform ultimate boundedness for perturbed systems. This ensures robustness against external disturbances with explicit performance guarantees. Simulations demonstrate the benefits of our approach.

Robust Self-Triggered Control Approaches Optimizing Sampling Sequences with Synchronous Measurements

TL;DR

The paper tackles resource-efficient control for linear systems by developing self-triggered sampling schemes that precompute the next sampling horizon to maximize inter-sampling intervals while preserving stability. It presents both online and offline variants for perturbation-free and perturbed (bounded disturbance) cases, establishing exponential stability via Lyapunov LMIs and global uniform ultimate boundedness (GUUB) with disturbance handling. Key contributions include horizon-based optimization over finite horizons, conic-region offline partitioning, and corresponding algorithms (Schur-LMI conditions and S-procedure-based LMIs) that guarantee stability or GUUB. The work demonstrates, through simulations, that substantial reductions in sampling frequency are achievable without compromising performance, making the approach suitable for embedded and networked control systems under tight computational and communication constraints.

Abstract

Feedback control algorithms traditionally rely on periodic execution on digital platforms. While this simplifies design and analysis, it often leads to inefficient resource usage (e.g., CPU, network bandwidth) in embedded control and shared networks. This work investigates self-triggering implementations of linear controllers in sampled-data systems with synchronous measurements. Our approach precomputes the next sampling sequence over a finite horizon based on current state information. We introduce a novel optimal self-triggering scheme that guarantees exponential stability for unperturbed systems and global uniform ultimate boundedness for perturbed systems. This ensures robustness against external disturbances with explicit performance guarantees. Simulations demonstrate the benefits of our approach.

Paper Structure

This paper contains 32 sections, 4 theorems, 57 equations, 12 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. System Description and Problem Statement
  3. System Description
  4. Motivational Example
  5. System Reformulation
  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. Main Results: Perturbed Case
  16. ...and 17 more sections

Key Result

Proposition 1

Consider a scalar $\beta>0$ 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 $\beta/2$.

Figures (12)

  • Figure 1: Evolution of the modulus of the maximum eigenvalue ${\tilde{A}}_{(T_h)}$ with respect to $T_h$
  • Figure 5: System state discretization using variable sequences
  • Figure 6: Covering the state space of dimension 2 with $N$ conic regions $\mathcal{R}_c, c \in \{1,\cdots,N\}$
  • Figure 7: The illustration of three regions $\mathcal{E}(P,1)$, $\mathcal{E}(P,\mu)$, and $\mathcal{B}(0,\psi)$.
  • Figure 8: Step Variations, Evolution of the system's states and Lyapunov function using variable sampling steps and horizons with a decay rate $\beta=0$
  • ...and 7 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