Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays

The problem of robust tracking and model following is considered for a class of linear systems with multiple delayed state perturbations, time-varying uncertain parameters, and disturbance. In this note, it is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances, are unknown. An improved adaptation law with σ-modification is proposed to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a class of continuous memoryless state feedback controllers is constructed for robust tracking of dynamical signals. The proposed adaptive robust tracking controller can guarantee that the tracking error decreases asymptotically to zero in the presence of multiple delayed state perturbations, time-varying uncertain parameters, and disturbance. In addition, it is also shown that this improved adaptation law with σ-modification can be applied to the general adaptive control problems to obtain some more exact control results. Finally, a numerical example is given to demonstrate the validity of the results.