Non-linear vehicle domain of attraction analysis using Sum-of-Squares programming

Non-linear lateral stability of a vehicle is considered. The region of attraction is estimated using Sum of Squares (SOS) programming and compared to previous results from the literature. Parametric studies are then carried out to analyse their influence on the stability region. The vehicle in both cornering and straight line motion is considered.

[1]  P. Olver.  Nonlinear Systems , 2013 .

[2]  Andrew Packard,et al.  Stability Region Analysis Using Polynomial and Composite Polynomial Lyapunov Functions and Sum-of-Squares Programming , 2008, IEEE Transactions on Automatic Control.

[3]  Ufuk Topcu,et al.  Local stability analysis using simulations and sum-of-squares programming , 2008, Autom..

[4]  P. Parrilo.  Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .

[5]  Z. Jarvis-Wloszek,et al.  Lyapunov Based Analysis and Controller Synthesis for Polynomial Systems using Sum-of-Squares Optimization , 2003 .

[6]  Graziano Chesi,et al.  LMI Techniques for Optimization Over Polynomials in Control: A Survey , 2010, IEEE Transactions on Automatic Control.

[7]  A. Garulli,et al.  Positive Polynomials in Control , 2005 .

[8]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[9]  A. Papachristodoulou.  Scalable analysis of nonlinear systems using convex optimization , 2005 .

[10]  Sobhan Sadri,et al.  Stability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponents , 2013 .

[11]  Johan Löfberg,et al.  Pre- and Post-Processing Sum-of-Squares Programs in Practice , 2009, IEEE Transactions on Automatic Control.

[12]  Nong Zhang,et al.  Investigation into untripped rollover of light vehicles in the modified fishhook and the sine maneuvers. Part I: Vehicle modelling, roll and yaw instability , 2008 .

[13]  D. N. Shields.  The behaviour of optimal Lyapunov functions , 1975 .

[14]  Jeffrey C. Huston,et al.  Estimating Lateral Stability Region of a Nonlinear 2 Degree-of-Freedom Vehicle , 1998 .

[15]  K. Ramasubramanian,et al.  A comparative study of computation of Lyapunov spectra with different algorithms , 1999, chao-dyn/9909029.

[16]  Jang Moo Lee,et al.  Estimation of the stability region of a vehicle in plane motion using a topological approach , 2002 .

[17]  Hans B. Pacejka,et al.  Tire and Vehicle Dynamics , 1982 .

[18]  J. C. Huston,et al.  Nonlinear Lateral Stability Analysis of Road Vehicles Using Liapunov's Second Method , 1984 .

[19]  Christine Qiong Wu,et al.  Lateral stability analysis of on-road vehicles using Lyapunov's direct method , 2012, 2012 IEEE Intelligent Vehicles Symposium.