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Robust Safety-Critical Control for Systems with Sporadic Measurements and Dwell Time Constraints

Joseph Breeden, Luca Zaccarian, Dimitra Panagou

TL;DR

This work addresses safety guarantees for dynamical systems subjected to disturbances and sporadic state measurements. It extends Control Barrier Function theory to robust timed CBFs within a hybrid framework that accommodates both impulsive and continuous actuators and an open-loop observer, using prediction functions to bound future uncertainty. The key contributions are the formal RIT-CBF and RT-CBF definitions, horizon-based online safety conditions, and explicit handling of measurement delays and dwell-time constraints, demonstrated on satellite rendezvous and orbit-stationkeeping scenarios. The approach enables forward-invariant safety under limited telemetry, with potential applicability to other infrequently measured safety-critical systems.

Abstract

This paper presents extensions of control barrier function (CBF) theory to systems with disturbances wherein a controller only receives measurements infrequently and operates open-loop between measurements, while still satisfying state constraints. The paper considers both impulsive and continuous actuators, and models the actuators, measurements, disturbances, and timing constraints as a hybrid dynamical system. We then design an open-loop observer that bounds the worst-case uncertainty between measurements. We develop definitions of CBFs for both actuation cases, and corresponding conditions on the control input to guarantee satisfaction of the state constraints. We apply these conditions to simulations of a satellite rendezvous in an elliptical orbit and autonomous orbit stationkeeping.

Robust Safety-Critical Control for Systems with Sporadic Measurements and Dwell Time Constraints

TL;DR

This work addresses safety guarantees for dynamical systems subjected to disturbances and sporadic state measurements. It extends Control Barrier Function theory to robust timed CBFs within a hybrid framework that accommodates both impulsive and continuous actuators and an open-loop observer, using prediction functions to bound future uncertainty. The key contributions are the formal RIT-CBF and RT-CBF definitions, horizon-based online safety conditions, and explicit handling of measurement delays and dwell-time constraints, demonstrated on satellite rendezvous and orbit-stationkeeping scenarios. The approach enables forward-invariant safety under limited telemetry, with potential applicability to other infrequently measured safety-critical systems.

Abstract

This paper presents extensions of control barrier function (CBF) theory to systems with disturbances wherein a controller only receives measurements infrequently and operates open-loop between measurements, while still satisfying state constraints. The paper considers both impulsive and continuous actuators, and models the actuators, measurements, disturbances, and timing constraints as a hybrid dynamical system. We then design an open-loop observer that bounds the worst-case uncertainty between measurements. We develop definitions of CBFs for both actuation cases, and corresponding conditions on the control input to guarantee satisfaction of the state constraints. We apply these conditions to simulations of a satellite rendezvous in an elliptical orbit and autonomous orbit stationkeeping.
Paper Structure (10 sections, 5 theorems, 33 equations, 4 figures)

This paper contains 10 sections, 5 theorems, 33 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Impulsive Control and Measurement Models
  3. Impulsive Control Explanation
  4. Hybrid Dynamical Model of Impulsive Control
  5. Measurements and Impulsive Open-Loop Observer
  6. Prediction Functions
  7. Control Law for Impulsive Actuators
  8. Control Law for Continuous Actuators
  9. Simulation Case Studies
  10. Conclusions

Key Result

Lemma 1

Let $(t_1,j_1)$ be the instant after the first jump according to $\mathcal{D}_m$ in eq:model_hybrid-eq:observer_hybrid. Then the solutions to eq:model_hybrid-eq:observer_hybrid satisfy $\|r(t,j) - \hat{r}(t,j)\| \leq \hat{\rho}_r(t,j)$ and $\| v(t,j) - \hat{v}(t,j)\| \leq \hat{\rho}_v(t,j)$ for all

Figures (4)

  • Figure 1: Visualization of the three timers (same units for both axes).
  • Figure 2: Block diagram of the impulsive system
  • Figure 3: Left: Plots of trajectories and uncertainties for the impulsive case study for various $T_M$, plotted in a rotating frame centered at the target, with the $x$ axis always along the target's radial direction. Note that the obstacles perform ellipses about the origin and are not static in this frame. Right: Plots of the real and estimated trajectories of the continuous case study inside a specified icosahedron.
  • Figure 4: Top: Plot of the 7 CBF values and estimates (shaded) for $T_M = 360$ s in the impulsive case study. Bottom: Plot of the max of the 20 CBF values and estimates in the continuous case study.

Theorems & Definitions (17)

  • Remark 1
  • Lemma 1
  • proof
  • Remark 2
  • Lemma 2
  • proof
  • Remark 3
  • Remark 4
  • Definition 1
  • Theorem 1
  • ...and 7 more