Nonlinear state-feedback design for vehicle lateral control using sum-of-squares programming

ABSTRACT

This work addresses the lateral stabilisation problem of four-wheels ground vehicles. The objective is to estimate the largest state-space region such that the closed-loop vehicle lateral stability can be guaranteed. Sum-of-squares (SOS) programming technique is applied to find these maximum invariant sets while accounting for steering and yaw moment input saturations. The algorithm allows the region of attraction (RoA) to be approximated by a level set of a Lyapunov function (LF) and the computation of polynomial state feedback control laws. The method is applied for both straight-line motion and cornering manoeuver. Finally, a Monte-Carlo analysis is presented to show that the proposed SOS-based methodology can be used as a valid analysis and design tool considering a real vehicle application.

Keywords:

• Region of attraction
• vehicle dynamics
• nonlinear control design
• sum-of-squares programming
• vehicle lateral stability
• polynomial systems

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors gratefully acknowledge the agencies FAPESP, CNPq, and FCT for the financial support. From Fapesp: Ph.D. grant (2018/05712-2), Project Auto-VERDE (2018/04905-1), and INCT-SAC Project (2014/50851-0), co-funded by CNPq (465755/2014-3). From CNPq: grant (305600/2017-6). From FCT: through IDMEC under LAETA, project UIDB/50022/2020. The mobility of A. M. Ribeiro has been possible with the Erasmus+ support (Project Reference: 552042-EM-1-2014-1-FR-ERA MUNDUS-EMA2) coordinated by CENTRALESUPELEC.${}^2$