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Event-Triggered Adaptive Taylor-Lagrange Control for Safety-Critical Systems

Shuo Liu, Wei Xiao, Christos G. Cassandras, Calin A. Belta

Abstract

This paper studies safety-critical control for nonlinear systems under sampled-data implementations of the controller. The recently proposed Taylor--Lagrange Control (TLC) method provides rigorous safety guarantees but relies on a fixed discretization-related parameter, which can lead to infeasibility or unsafety in the presence of input constraints and inter-sampling effects. To address these limitations, we propose an adaptive Taylor--Lagrange Control (aTLC) framework with an event-triggered implementation, where the discretization-related parameter defines the discretization time scale and is selected online as state-dependent rather than fixed. This enables the controller to dynamically balance feasibility and safety by adjusting the effective time scale of the Taylor expansion. The resulting controller is implemented as a sequence of Quadratic Programs (QPs) with input constraints. We further introduce a selection rule to choose the discretization-related parameter from a finite candidate set, favoring feasible inputs and improved safety. Simulation results on an adaptive cruise control (ACC) problem demonstrate that the proposed approach improves feasibility, guarantees safety, and achieves smoother control actions compared to TLC while requiring a single automatically tuned parameter.

Event-Triggered Adaptive Taylor-Lagrange Control for Safety-Critical Systems

Abstract

This paper studies safety-critical control for nonlinear systems under sampled-data implementations of the controller. The recently proposed Taylor--Lagrange Control (TLC) method provides rigorous safety guarantees but relies on a fixed discretization-related parameter, which can lead to infeasibility or unsafety in the presence of input constraints and inter-sampling effects. To address these limitations, we propose an adaptive Taylor--Lagrange Control (aTLC) framework with an event-triggered implementation, where the discretization-related parameter defines the discretization time scale and is selected online as state-dependent rather than fixed. This enables the controller to dynamically balance feasibility and safety by adjusting the effective time scale of the Taylor expansion. The resulting controller is implemented as a sequence of Quadratic Programs (QPs) with input constraints. We further introduce a selection rule to choose the discretization-related parameter from a finite candidate set, favoring feasible inputs and improved safety. Simulation results on an adaptive cruise control (ACC) problem demonstrate that the proposed approach improves feasibility, guarantees safety, and achieves smoother control actions compared to TLC while requiring a single automatically tuned parameter.

Paper Structure

This paper contains 11 sections, 6 theorems, 23 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Definitions and Preliminaries
  3. Problem Formulation and Approach
  4. Adaptive Taylor–Lagrange Control
  5. Event-Triggered aTLC with Adaptive Time Scale
  6. Forward Invariance with Adaptive Time Scale
  7. Feasibility Characterization via Value Function
  8. Adaptive Selection of Time Scale
  9. Complexity Analysis
  10. Case Study and Simulations
  11. Conclusion and Future Work

Key Result

Theorem 1

Let $h(\boldsymbol{x})$ be a TLC function as defined in Def. def: TLC, and let the corresponding safe set $\mathcal{C}$ be defined as in eq: safety set. If $h(\boldsymbol{x}(t_0)) \ge 0$, then any Lipschitz continuous control input $\boldsymbol{u}(\xi)$ that satisfies the TLC condition in Def. def:

Figures (2)

  • Figure 3: Performance Comparison between TLC and aTLC in ACC. aTLC achieves improved feasibility while maintaining safety (i.e., avoiding violations of $h(\boldsymbol{x})\ge 0$) compared to TLC when $c_d$ is small.
  • Figure 4: aTLC improves feasibility and ensures safety compared to TLC, while achieving performance comparable to a well-tuned HOCBF despite requiring only a single parameter..

Theorems & Definitions (19)

  • Definition 1: Class $\@fontswitch\mathcal{K}$ function Khalil:1173048
  • Definition 2
  • Definition 3
  • Definition 4: Taylor--Lagrange Control (TLC) xiao2025taylor
  • Theorem 1: xiao2025taylor
  • Definition 5: CLF ames2012control
  • Definition 6: Adaptive Taylor--Lagrange Control (aTLC)
  • Theorem 2
  • proof
  • Theorem 3: Forward Invariance under Event-Triggered aTLC
  • ...and 9 more