Adaptive control for a class of nonlinear time-delay systems preceded by unknown hysteresis

Abstract

In this article, a robust adaptive neural dynamic surface control is proposed for a class of time-delay nonlinear systems preceded by saturated hystereses. Compared with the present schemes of dealing with time delay and hystereses input, the main advantages of the proposed scheme are that the prespecified transient and steady-state performance of tracking error can be guaranteed, the computational burden can be greatly reduced and the explosion of complexity problem inherent in backstepping control can be eliminated. Moreover, the utilisation of saturated-type Prandtl–Ishlinskii model makes our scheme more applicable. It is proved that the new scheme can guarantee all the closed-loop signals semiglobally uniformly ultimate bounded. Simulation results are presented to demonstrate the validity of the proposed scheme.

Keywords:

• saturated hystereses
• dynamic surface control
• unknown time-delay
• prespecified tracking error

Acknowledgements

Work supported by NSF of China under Grant 60874044 and 91016006.

Notes

Notes

1. The derivation of Q ₁(x ₁), Q ₁(x _1τ) below in this step and , in the next steps is just for the purpose of making the expression more succinct.

2. Note that by Ge and Tee (2007), where ϵ is a positive constant.

3. By Ge and Tee (2007), the compact set is defined as for i = 1, … , n. Note that for any , the inequality holds with ϵ _i  > 0.