Existence, stability and robustness analysis of limit cycles in hybrid anti-lock braking systems

Abstract

We investigate the stability and robustness properties of anti-lock braking systems (ABS) based on actuators with on/off dynamics. Namely, we propose a hybrid ABS controller which gives rise to an asymptotically stable limit cycle on the wheel slip. The proposed approach allows to derive exact information on the maximum allowable uncertainty in the measured variables which guarantee the cycle stability. Moreover, a structural stability analysis is performed with respect to different road conditions and to the actuator rate limit.

Keywords:

• vehicle dynamics
• automotive control
• limit cycles
• hybrid systems
• non-smooth dynamics

Acknowledgements

The authors acknowledge the support by MIUR project ‘Identification and Adaptive Control of industrial systems’, MIUR project ‘Advanced Methodologies for Control of Hybrid Systems’ and EU project SICONOS IST-31712.

Notes

Notes

1. for a generic dynamical system with state x ∈ ℝ ⁿ , the orbit forward in time is defined as Φ(t − t ₀, x(t ₀)), where t ₀ is the initial time and x(t ₀) the initial conditions, (Wiggins 2003).

2. The boundary of a set ℐ is denoted by ∂ℐ.