Progressive Barrier Lyapunov Functions for Nonlinear Constrained Control Systems

TL;DR

This paper proposes the Progressive Barrier Lyapunov Function (p-BLF), a novel approach for constrained nonlinear control that ensures smooth, minimal control effort in unconstrained regions and progressively increases effort near boundaries, enhancing stability and reducing chattering.

Contribution

The paper introduces the p-BLF, providing a new smooth transition method for control effort in constrained systems, with theoretical guarantees and two functional forms for different constraint types.

Findings

p-BLF maintains system states within constraints.

The method reduces control chattering and improves stability.

Simulation results confirm effectiveness in nonlinear control.

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.