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arXiv · 2411.06288

Progressive Barrier Lyapunov Functions for Nonlinear Constrained Control Systems

Hamed Rahimi Nohooji·Holger Voos
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Abstract

This paper introduces the Progressive Barrier Lyapunov Function (p-BLF) for output- and full-state-constrained nonlinear control systems. Unlike traditional BLF methods, where control effort continuously increases as the state approaches the constraint boundaries, the p-BLF maintains minimal control effort in unconstrained regions and increases it progressively toward the boundaries. In contrast to previous methods with predefined safe zones and abrupt control activation, the p-BLF provides a smooth transition, improving continuity in the control response and enhancing stability by reducing chattering. Two forms of the p-BLF, logarithmic-based and rational-based, are developed to handle systems with either output constraints or full-state constraints. Theoretical analysis guarantees that all system states remain within the defined constraints, ensuring boundedness and stability of the closed-loop system. Simulation results validate the effectiveness of the proposed method in constrained nonlinear control.

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BibTeXRIS

Hamed Rahimi Nohooji, Holger Voos. 2024-11-09. Progressive Barrier Lyapunov Functions for Nonlinear Constrained Control Systems. https://arxiv.org/abs/2411.06288

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