Robust adaptive control of non-linear time-delay systems with saturation constraints

In this study, a robust adaptive control strategy is presented for a class of uncertain time-delay non-linear systems in the presence of non-symmetric saturation constraints. On the one hand, an auxiliary system is constructed to reduce the negative effects cased by possible saturations, and the following stability proof ensures the theoretical strictness; the unknown time delays, on the other hand, are compensated by choosing appropriate Lyapunov-Krasovskii functions. Furthermore, the hyperbolic tangent functions are employed to efficiently avoid the controller singularity problem encountered in Lyapunov synthesis, and it is proved that the proposed controller design method is able to guarantee semi-global uniform ultimate boundedness of all the signals in the closed-loop system. Finally, an example simulation is conducted to verify the effectiveness of theoretic results.