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Robust Safety Filters for Lipschitz-Bounded Adaptive Closed-Loop Systems with Structured Uncertainties

Johannes Autenrieb, Peter A. Fisher, Anuradha Annaswamy

Abstract

Adaptive control provides closed-loop stability and reference tracking for uncertain dynamical systems through online parameter adaptation. These properties alone, however, do not ensure safety in the sense of forward invariance of state constraints, particularly during transient phases of adaptation. Control barrier function (CBF)-based safety filters have been proposed to address this limitation, but existing approaches often rely on conservative constraint tightening or static safety margins within quadratic program formulations. This paper proposes a reference-based adaptive safety framework for systems with structured parametric uncertainty that explicitly accounts for transient plant-reference mismatch. Safety is enforced at the reference level using a barrier-function-based filter, while adaptive control drives the plant to track the safety-certified reference. By exploiting Lipschitz bounds on the closed-loop error dynamics, a robust CBF condition is derived and reformulated as a convex second-order cone program (SOCP). The resulting approach reduces conservatism while preserving formal guarantees of forward invariance, stability, and tracking.

Robust Safety Filters for Lipschitz-Bounded Adaptive Closed-Loop Systems with Structured Uncertainties

Abstract

Adaptive control provides closed-loop stability and reference tracking for uncertain dynamical systems through online parameter adaptation. These properties alone, however, do not ensure safety in the sense of forward invariance of state constraints, particularly during transient phases of adaptation. Control barrier function (CBF)-based safety filters have been proposed to address this limitation, but existing approaches often rely on conservative constraint tightening or static safety margins within quadratic program formulations. This paper proposes a reference-based adaptive safety framework for systems with structured parametric uncertainty that explicitly accounts for transient plant-reference mismatch. Safety is enforced at the reference level using a barrier-function-based filter, while adaptive control drives the plant to track the safety-certified reference. By exploiting Lipschitz bounds on the closed-loop error dynamics, a robust CBF condition is derived and reformulated as a convex second-order cone program (SOCP). The resulting approach reduces conservatism while preserving formal guarantees of forward invariance, stability, and tracking.
Paper Structure (9 sections, 3 theorems, 44 equations, 4 figures)

This paper contains 9 sections, 3 theorems, 44 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries & Problem Formulation
  3. Preliminaries
  4. Problem Formulation
  5. Adaptive Closed-Loop System Design
  6. Robust Safety for Lipschitz-Bounded Adaptive Closed-Loop Systems with Structured Uncertainties
  7. SOCP-based safe reference signal generation
  8. Simulations
  9. Conclusions

Key Result

Theorem 1

Given a set $S \subset \chi$, defined via the associated CBF as in Safe_set_1, any Lipschitz continuous controller ${k}({x}) \in K_{S}({x})$ with renders the system NonlinearPlant forward invariant within $S$XU2015.

Figures (4)

  • Figure 1: Illustration of the proposed robust safety-critical adaptive control concept for systems with structured uncertainties.
  • Figure 2: Concept of the proposed safe adaptive control architecture.
  • Figure 3: 3D quadrotor trajectories for different safety filters under model mismatch.
  • Figure 4: Planar projections of the trajectories for different safety filters under model mismatch.

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Remark 1