Guaranteed performance in semi global trajectory tracking for matched disturbance nonlinear systems

Abstract

In this article, we present a semi global trajectory tracking approach that guarantees a priori computable L ₂ and L _∞ performance bounds for matched disturbance control affine systems. The proposed controller is derived by combining a standard inverse control technique with an extended nonlinear robust state feedback. The latter is based on a control Lyapunov function used for stabilising one operating point inside the considered state space. A difference gradient formulation of this Lyapunov function is then applied to prove stabilisation along any trajectory in the considered state space. Results for L ₂ and L _∞ bounded disturbances will be presented and further extended to the case of actuator uncertainties and disturbance offsets. The theoretical contributions are verified applying them to a numerical example.

Keywords:

• robust control
• trajectory tracking
• feedforward control

Acknowledgements

The authors gratefully acknowledge the sponsoring of this work by the COMET K2 Center Austrian Center of Competence in Mechatronics (ACCM).