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A Robust, Efficient Predictive Safety Filter

Wenceslao Shaw Cortez, Jan Drgona, Draguna Vrabie, Mahantesh Halappanavar

TL;DR

This work confronts the challenge of ensuring hard safety for discrete-time, nonlinear, time-varying systems under bounded disturbances. It develops a robust, horizon-based predictive safety filter built on discrete-time high-order barrier functions (HODCBF) and leverages an event-triggered scheme to reduce online computation, while supporting a 1-step robust variant for faster operation. The framework guarantees forward invariance of the safe set under disturbances and demonstrates feasibility and safety through three numerical examples with a differentiable predictive control (DPC) policy as the nominal controller. The combination of robust safety guarantees, horizon-based planning, and event-triggered execution provides a practical, scalable approach for safety-critical learning-based control on resource-constrained platforms. This has significant implications for deploying learning-enabled controllers in real-time, safety-critical applications such as process and building systems.

Abstract

In this paper, we propose a novel predictive safety filter that is robust to bounded perturbations and is implemented in an even-triggered fashion to reduce online computation. The proposed safety filter extends upon existing work to reject disturbances for discrete-time, time-varying nonlinear systems with time-varying constraints. The safety filter is based on novel concepts of robust, discrete-time barrier functions and can be used to filter any control law. Here, we use the safety filter in conjunction with Differentiable Predictive Control (DPC) as a promising offline learning-based policy optimization method. The approach is demonstrated on a two-tank system, building, and single-integrator example.

A Robust, Efficient Predictive Safety Filter

TL;DR

This work confronts the challenge of ensuring hard safety for discrete-time, nonlinear, time-varying systems under bounded disturbances. It develops a robust, horizon-based predictive safety filter built on discrete-time high-order barrier functions (HODCBF) and leverages an event-triggered scheme to reduce online computation, while supporting a 1-step robust variant for faster operation. The framework guarantees forward invariance of the safe set under disturbances and demonstrates feasibility and safety through three numerical examples with a differentiable predictive control (DPC) policy as the nominal controller. The combination of robust safety guarantees, horizon-based planning, and event-triggered execution provides a practical, scalable approach for safety-critical learning-based control on resource-constrained platforms. This has significant implications for deploying learning-enabled controllers in real-time, safety-critical applications such as process and building systems.

Abstract

In this paper, we propose a novel predictive safety filter that is robust to bounded perturbations and is implemented in an even-triggered fashion to reduce online computation. The proposed safety filter extends upon existing work to reject disturbances for discrete-time, time-varying nonlinear systems with time-varying constraints. The safety filter is based on novel concepts of robust, discrete-time barrier functions and can be used to filter any control law. Here, we use the safety filter in conjunction with Differentiable Predictive Control (DPC) as a promising offline learning-based policy optimization method. The approach is demonstrated on a two-tank system, building, and single-integrator example.
Paper Structure (19 sections, 6 theorems, 27 equations, 9 figures, 2 algorithms)

This paper contains 19 sections, 6 theorems, 27 equations, 9 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Notation and Preliminaries
  4. Problem Formulation
  5. Robust Predictive Safety Filter
  6. Robust Barrier Functions
  7. Predictive Control
  8. Analysis
  9. Extensions and Implementation
  10. Event-triggered control
  11. Efficient 1-step Robust Safety Filter
  12. Numerical Examples
  13. Two-Tank Example
  14. Building Example
  15. Simple Example (1-step Safety Filter)
  16. ...and 4 more sections

Key Result

Proposition 1

Consider the system eq:nonlinear system discrete for which Assumption asm:lipschitz f holds. Given a function $b: \mathbb{R}^n\times \mathbb{N} \to \mathbb{R}$ satisfying Assumption asm:lipschitz.1, let $\hat{\mathcal{K}}_{N|k}$, $\delta \hat{b}_{N|k}$, and $\mathcal{X}(k)$ be defined by eq:predict

Figures (9)

  • Figure 1: Schematics of the proposed event-triggered robust predictive safety filter combined with learning-based policy.
  • Figure 2: (Two-tank example) Comparison of trajectories for 'DPC' and 'DPC+SF' implementations with the proposed robust safety filter on the perturbed two-tank system with $\bar{w} = 0.00001$.
  • Figure 3: (Two-tank example) Comparison of trajectories for 'DPC' and 'DPC+SF' implementations with the proposed robust safety filter on the perturbed two-tank system with $\bar{w} = 0.001$.
  • Figure 4: (Two-tank example) Results for predictive safety filter of Wabersich2022a for 'DPC' and 'DPC+SF' implementations on the perturbed two-tank system with $\bar{w} = 0.001$.
  • Figure 5: Estimate of environmental perturbations on the building, $\hat{\bm{w}}(k)$.
  • ...and 4 more figures

Theorems & Definitions (21)

  • Remark 1
  • Definition 1
  • Remark 2
  • Proposition 1
  • proof
  • Remark 3
  • Remark 4
  • Theorem 1
  • proof
  • Remark 5: Multiple constraints
  • ...and 11 more