Tracking trajectories of feedforward systems: application to the cart-pendulum system

The objective of the work is twofold. A first part is devoted to the problem of tracking trajectories of feedforward systems. A family of the time-varying state feedbacks which globally uniformly asymptotically and locally exponentially stabilize trajectories which are not necessarily periodic functions of the time is exhibited. Strict Lyapunov functions are constructed. In a second part, the problem of tracking a trajectory of the practical system called cart-pendulum system is solved.

[1]  P. Kokotovic,et al.  Adaptive tracking for feedback linearizable SISO systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[2]  A. Isidori.  Nonlinear Control Systems , 1985 .

[3]  Eduardo D. Sontag,et al.  Remarks on finite gain stabilizability of linear systems subject to input saturation , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[4]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[5]  A. Teel.  A nonlinear small gain theorem for the analysis of control systems with saturation , 1996, IEEE Trans. Autom. Control..

[6]  L. Praly,et al.  Adding an integration and global asymptotic stabilization of feedforward systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[7]  B. Paden,et al.  A different look at output tracking: control of a VTOL aircraft , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[8]  K.Y. Pettersen,et al.  Global practical stabilization and tracking for an underactuated ship-a combined averaging and backs , 1998 .

[9]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[10]  Frédéric Mazenc,et al.  Asymptotic tracking of a reference state for systems with a feedforward structure , 2000, Autom..

[11]  Romeo Ortega,et al.  Passivity-based Control of Euler-Lagrange Systems , 1998 .

[12]  Eduardo Sontag,et al.  On Finite-Gain Stabilizability of Linear Systems Subject to Input Saturation , 1996 .