Adaptive tracking control for a class of non-autonomous systems containing time-varying uncertainties with unknown bounds

This paper proposes an adaptive tracking controller based on function approximation technique (FAT) for a class of MIMO non-autonomous systems with time-varying uncertainties. Since it is assumed that the variation bounds of some of the uncertainties are unavailable, conventional robust strategies cannot be applied. Besides, due to their time-varying nature, traditional adaptive schemes are infeasible. In this paper, an adaptive controller is developed for MIMO square systems such that bounded tracking performance can be obtained and the singularity problem of the control input can be totally avoided, if the bounds of the uncertainties in the input-coupling matrix are available. Rigorous proof of the closed-loop stability and the performance analysis of the transient state are derived based on the Lapunov-like approach. Some simulation examples are performed to verify the effectiveness of the proposed method.