Nonlinear analysis of vehicle control actuations based on controlled invariant sets

Beal, C.E. and Gerdes, J.C. (2013). Model predictive control for vehicle stabilization at the limits of handling, IEEE Transactions on Control Systems Technology21(4): 1258–1269.10.1109/TCST.2012.2200826Search in Google Scholar

Cairano, S., Tseng, H.E., Bernardini, D. and Bemporad, A. (2013). Vehicle yaw stability control by coordinated active front steering and differential braking in the tire sideslip angles domain, IEEE Transactions on Control Systems Technology21(4): 1236–1248.10.1109/TCST.2012.2198886Search in Google Scholar

Carvalho, A., Palmieri, G., Tseng, H., Glielmo, L. and Borrelli, F. (2013). Robust vehicle stability control with an uncertain driver model, European Control Conference, Zurich, Switzerland, pp. 440–445.Search in Google Scholar

de Wit, C.C., Olsson, H., Astrom, K.J. and Lischinsky, P. (1995). A new model for control of systems with friction, IEEE Transactions on Automatic Control40(3): 419–425.10.1109/9.376053Search in Google Scholar

Grip, H., Imsland, L., Johansen, T., Fossen, T., Kalkkuhl, J. and Suissa, A. (2008). Nonlinear vehicle side-slip estimation with friction adaptation, Automatica44(11): 611–622.10.1016/j.automatica.2007.06.017Search in Google Scholar

Gustafsson, F. (1997). Slip-based tire-road friction estimation, Automatica33(6): 1087–1099.10.1016/S0005-1098(97)00003-4Search in Google Scholar

Jarvis-Wloszek, Z. (2003). Lyapunov Based Analysis and Controller Synthesis for Polynomial Systems using Sum-of-Squares Optimization, Ph.D. Thesis, University of California, Berkeley, CA.Search in Google Scholar

Jarvis-Wloszek, Z., Feeley, R., Tan, W., Sun, K. and Packard, A. (2003). Some controls applications of sum of squares programming, 42nd IEEE Conference on Decision and Control, Maui, HI, USA, Vol. 5, pp. 4676–4681.Search in Google Scholar

Jianyong, W., Houjun, T., Shaoyuan, L. and Wan, F. (2007). Improvement of vehicle handling and stability by integrated control of four wheel steering and direct yaw moment, 26th Chinese Control Conference, Zhangjiajie, China, pp. 730–735.Search in Google Scholar

Khelassi, A., Theilliol, D. and Weber, P. (2011). Reconfigurability analysis for reliable fault-tolerant control design, International Journal of Applied Mathematics and Computer Science21(3): 431–439, DOI: 10.2478/v10006-011-0032-z.10.2478/v10006-011-0032-zSearch in Google Scholar

Kiencke, U. and Nielsen, L. (2000). Automotive Control Systems for Engine, Driveline and Vehicle, Springer, New York, NY.10.1088/0957-0233/11/12/708Search in Google Scholar

Kim, D., Peng, H., Bai, S. and Maguire, J. (2007). Control of integrated powertrain with electronic throttle and automatic transmission, IEEE Transactions on Control Systems Technology15(3): 474–482.10.1109/TCST.2007.894641Search in Google Scholar

Korda, M., Henrion, D. and Jones, C.N. (2013). Convex computation of the maximum controlled invariant set for discrete-time polynomial control systems, Conference on Decision and Control, Firenze, Italy, pp. 7107–7112.Search in Google Scholar

Kritayakirana, K. and Gerdes, J. (2012a). Using the centre of percussion to design a steering controller for an autonomous race car, Vehicle System Dynamics50(Supp1): 33–51.10.1080/00423114.2012.672842Search in Google Scholar

Kritayakirana, K. and Gerdes, J.C. (2012b). Autonomous vehicle control at the limits of handling, International Journal of Vehicle Autonomous Systems10(4): 271–296.10.1504/IJVAS.2012.051270Search in Google Scholar

Lasserre, J.B. (2007). Sum of squares approximation of nonnegative polynomials, SIAM Journal on Optimization49(4): 651–669.10.1137/070693709Search in Google Scholar

Löfberg, J. (2009). Pre- and post-processing sum-of-squares programs in practice, IEEE Trans. on Automatic Control54(5): 1007–1011.Search in Google Scholar

Lu, J. and Filev, D. (2009). Multi-loop interactive control motivated by driver-in-the-loop vehicle dynamics controls: The framework, Conference on Decision and Control, Shanghai, China, pp. 3569–3574.Search in Google Scholar

Mastinu, G., Babbel, E., Lugner, P., Margolis, D., Mittermayr P. and Richter, B. (1994). Integrated controls of lateral vehicle dynamics, Vehicle System Dynamics23(Supp1): 358–377.10.1080/00423119308969527Search in Google Scholar

Németh, B. and Gáspár, P. (2011). Design of actuator interventions in the trajectory tracking for road vehicles, Conference on Decision and Control, Orlando, FL, USA, pp. 7434–7439.Search in Google Scholar

Németh, B. and Gáspár, P. (2013). Analysis of vehicle actuators based on reachable sets, European Control Conference, Zurich, Switzerland, pp. 3137–3142.Search in Google Scholar

Ono, E., Hattori, Y., Muragishi, Y. and Koibuchi, K. (2006). Vehicle dynamics integrated control for four-wheel-distributed steering and four-wheel-distributed traction/braking systems, Vehicle System Dynamics44(2): 139–151.10.1080/00423110500385790Search in Google Scholar

Pacejka, H.B. (2004). Tyre and Vehicle Dynamics, Elsevier Butterworth-Heinemann, Oxford.Search in Google Scholar

Palmieri, G., Barc, M., Glielmo, L., Tseng, E.H. and Borrelli, F. (2011). Robust vehicle lateral stabilization via set-based methods for uncertain piecewise affine systems: Experimental results, 50th IEEE Conference on Decision and Control, Orlando, FL, USA, pp. 3252–3257.Search in Google Scholar

Palmieri, G., Baric, M., Glielmo, L. and Borrelli, F. (2012). Robust vehicle lateral stabilisation via set-based methods for uncertain piecewise affine systems, Vehicle System Dynamics50(6): 861–882.10.1080/00423114.2012.666353Search in Google Scholar

Papachristodoulou, A. and Prajna, S. (2005). Analysis of non-polynomial systems using the sum of squares decomposition, in D. Henrion and A. Garulli (Eds.), Positive Polynomials in Control, Springer-Verlag, Berlin/Heidelberg, pp. 23–43.10.1007/10997703_2Search in Google Scholar

Parrilo, P. (2003). Semidefinite programming relaxations for semialgebraic problems, Mathematical Programming B96(2): 293–320.10.1007/s10107-003-0387-5Search in Google Scholar

Poussot-Vassal, C., Sename, O., Dugard, L., Gáspár, P., Szabó, Z. and Bokor, J. (2008). A new semi-active suspension control strategy through LPV technique, Control Engineering Practice16(12): 1519–1534.10.1016/j.conengprac.2008.05.002Search in Google Scholar

Prajna, S., Papachristodoulou, A. and Wu., F. (2004). Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based approach, 5th IEEE Asian Control Conference, Melbourne, Australia, Vol. 1, pp. 157–165.Search in Google Scholar

Sadri, S. and Wu, C. (2013). Stability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponents, Vehicle System Dynamics51(6): 906–924.10.1080/00423114.2013.771785Search in Google Scholar

Scherer, C.W. and Hol, C.W.J. (2006). Matrix sum-of-squares relaxations for robust semi-definite programs, Mathematical Programming107(1): 189–211.10.1007/s10107-005-0684-2Search in Google Scholar

Sontag, E.D. (1989). A “universal” construction of Artstein’s theorem on nonlinear stabilization, Systems & Control Letters13(2): 117–123.10.1016/0167-6911(89)90028-5Search in Google Scholar

Summers, E., Chakraborty, A., Tan, W., Topcu, U., Seiler, P., Balas, G. and Packard, A. (2003). Quantitative local l₂-gain and reachability analysis for nonlinear systems, International Journal of Robust and Nonlinear Control23(10): 1115–1135.10.1002/rnc.2948Search in Google Scholar

Tan, W. and Packard, A. (2008). Stability region analysis using polynomial and composite polynomial Lyapunov functions and sum-of-squares programming, IEEE Transactions on Automatic Control53(2): 565–571.10.1109/TAC.2007.914221Search in Google Scholar

Topcu, U. and Packard, A. (2009). Local robust performance analysis for nonlinear dynamical systems, American Control Conference, St. Louis, MO, USA, pp. 784–789.Search in Google Scholar

Yetendje, A., Seron, M.M. and De Doná, J.D. (2012). Robust multisensor fault tolerant model-following MPC design for constrained systems, International Journal of Applied Mathematics and Computer Science22(1): 211–223, DOI: 10.2478/v10006-012-0016-7.10.2478/v10006-012-0016-7Search in Google Scholar

Yu, F., Li, D. and Crolla, D. (2008). Integrated vehicle dynamics control: State-of-the art review, IEEE Vehicle Power and Propulsion Conference, Harbin, China, pp. 1–6.Search in Google Scholar

Zhang, S., Zhang, T. and Zhou, S. (2009). Vehicle stability control strategy based on active torque distribution and differential braking, Conference on Measuring Technology and Mechatronics Automation, Zhangjiajie, Hunan, China, pp. 922–925.Search in Google Scholar